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Suma de la serie:
(3^n+2^n)/6^n
7+k
(4x)^(2n)
3^n/n^2
Expresiones idénticas
cos(n*x)/n^ tres
coseno de (n multiplicar por x) dividir por n al cubo
coseno de (n multiplicar por x) dividir por n en el grado tres
cos(n*x)/n3
cosn*x/n3
cos(n*x)/n³
cos(n*x)/n en el grado 3
cos(nx)/n^3
cos(nx)/n3
cosnx/n3
cosnx/n^3
cos(n*x) dividir por n^3
Expresiones semejantes
(cos(n*x))/(n^3)
Expresiones con funciones
Coseno cos
cos2n
cos(pin)
cosпn
cosπn.
cos(sqrt(n))/n!

Suma de la serie cos(n*x)/n^3

Solución

Ha introducido [src]

 1000         
____          
\   `         
 \    cos(n*x)
  \   --------
  /       3   
 /       n    
/___,         
n = 1

$$\sum_{n=1}^{1000} \frac{\cos{\left(n x \right)}}{n^{3}}$$

Sum(cos(n*x)/n^3, (n, 1, 1000))

Respuesta [src]

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---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ---------- + ----------- + cos(x)
   8          27         64        125        216        343        512        729         1000        1331        1728        2197        2744        3375        4096        4913        5832        6859        8000        9261       10648       12167       13824       15625       17576       19683       21952       24389       27000       29791       32768       35937       39304       42875       46656       50653       54872       59319       64000       68921       74088       79507       85184       91125       97336       103823      110592      117649      125000      132651      140608      148877      157464      166375      175616      185193      195112      205379      216000      226981      238328      250047      262144      274625      287496      300763      314432      328509      343000      357911      373248      389017      405224      421875      438976      456533      474552      493039      512000      531441      551368      571787      592704      614125      636056      658503      681472      704969      729000      753571      778688      804357      830584      857375      884736      912673      941192      970299     1000000      1030301      1061208      1092727      1124864      1157625      1191016      1225043      1259712      1295029      1331000      1367631      1404928      1442897      1481544      1520875      1560896      1601613      1643032      1685159      1728000      1771561      1815848      1860867      1906624      1953125      2000376      2048383      2097152      2146689      2197000      2248091      2299968      2352637      2406104      2460375      2515456      2571353      2628072      2685619      2744000      2803221      2863288      2924207      2985984      3048625      3112136      3176523      3241792      3307949      3375000      3442951      3511808      3581577      3652264      3723875      3796416      3869893      3944312      4019679      4096000      4173281      4251528      4330747      4410944      4492125      4574296      4657463      4741632      4826809      4913000      5000211      5088448      5177717      5268024      5359375      5451776      5545233      5639752      5735339      5832000      5929741      6028568      6128487      6229504      6331625      6434856      6539203      6644672      6751269      6859000      6967871      7077888      7189057      7301384      7414875      7529536      7645373      7762392      7880599      8000000      8120601      8242408      8365427      8489664      8615125      8741816      8869743      8998912      9129329      9261000      9393931      9528128      9663597      9800344      9938375      10077696     10218313     10360232     10503459     10648000     10793861     10941048     11089567     11239424     11390625     11543176     11697083     11852352     12008989     12167000     12326391     12487168     12649337     12812904     12977875     13144256     13312053     13481272     13651919     13824000     13997521     14172488     14348907     14526784     14706125     14886936     15069223     15252992     15438249     15625000     15813251     16003008     16194277     16387064     16581375     16777216     16974593     17173512     17373979     17576000     17779581     17984728     18191447     18399744     18609625     18821096     19034163     19248832     19465109     19683000     19902511     20123648     20346417     20570824     20796875     21024576     21253933     21484952     21717639     21952000     22188041     22425768     22665187     22906304     23149125     23393656     23639903     23887872     24137569     24389000     24642171     24897088     25153757     25412184     25672375     25934336     26198073     26463592     26730899     27000000     27270901     27543608     27818127     28094464     28372625     28652616     28934443     29218112     29503629     29791000     30080231     30371328     30664297     30959144     31255875     31554496     31855013     32157432     32461759     32768000     33076161     33386248     33698267     34012224     34328125     34645976     34965783     35287552     35611289     35937000     36264691     36594368     36926037     37259704     37595375     37933056     38272753     38614472     38958219     39304000     39651821     40001688     40353607     40707584     41063625     41421736     41781923     42144192     42508549     42875000     43243551     43614208     43986977     44361864     44738875     45118016     45499293     45882712     46268279     46656000     47045881     47437928     47832147     48228544     48627125     49027896     49430863     49836032     50243409     50653000     51064811     51478848     51895117     52313624     52734375     53157376     53582633     54010152     54439939     54872000     55306341     55742968     56181887     56623104     57066625     57512456     57960603     58411072     58863869     59319000     59776471     60236288     60698457     61162984     61629875     62099136     62570773     63044792     63521199     64000000     64481201     64964808     65450827     65939264     66430125     66923416     67419143     67917312     68417929     68921000     69426531     69934528     70444997     70957944     71473375     71991296     72511713     73034632     73560059     74088000     74618461     75151448     75686967     76225024     76765625     77308776     77854483     78402752     78953589     79507000     80062991     80621568     81182737     81746504     82312875     82881856     83453453     84027672     84604519     85184000     85766121     86350888     86938307     87528384     88121125     88716536     89314623     89915392     90518849     91125000     91733851     92345408     92959677     93576664     94196375     94818816     95443993     96071912     96702579     97336000     97972181     98611128     99252847     99897344    100544625    101194696    101847563    102503232    103161709    103823000    104487111    105154048    105823817    106496424    107171875    107850176    108531333    109215352    109902239    110592000    111284641    111980168    112678587    113379904    114084125    114791256    115501303    116214272    116930169    117649000    118370771    119095488    119823157    120553784    121287375    122023936    122763473    123505992    124251499    125000000    125751501    126506008    127263527    128024064    128787625    129554216    130323843    131096512    131872229    132651000    133432831    134217728    135005697    135796744    136590875    137388096    138188413    138991832    139798359    140608000    141420761    142236648    143055667    143877824    144703125    145531576    146363183    147197952    148035889    148877000    149721291    150568768    151419437    152273304    153130375    153990656    154854153    155720872    156590819    157464000    158340421    159220088    160103007    160989184    161878625    162771336    163667323    164566592    165469149    166375000    167284151    168196608    169112377    170031464    170953875    171879616    172808693    173741112    174676879    175616000    176558481    177504328    178453547    179406144    180362125    181321496    182284263    183250432    184220009    185193000    186169411    187149248    188132517    189119224    190109375    191102976    192100033    193100552    194104539    195112000    196122941    197137368    198155287    199176704    200201625    201230056    202262003    203297472    204336469    205379000    206425071    207474688    208527857    209584584    210644875    211708736    212776173    213847192    214921799    216000000    217081801    218167208    219256227    220348864    221445125    222545016    223648543    224755712    225866529    226981000    228099131    229220928    230346397    231475544    232608375    233744896    234885113    236029032    237176659    238328000    239483061    240641848    241804367    242970624    244140625    245314376    246491883    247673152    248858189    250047000    251239591    252435968    253636137    254840104    256047875    257259456    258474853    259694072    260917119    262144000    263374721    264609288    265847707    267089984    268336125    269586136    270840023    272097792    273359449    274625000    275894451    277167808    278445077    279726264    281011375    282300416    283593393    284890312    286191179    287496000    288804781    290117528    291434247    292754944    294079625    295408296    296740963    298077632    299418309    300763000    302111711    303464448    304821217    306182024    307546875    308915776    310288733    311665752    313046839    314432000    315821241    317214568    318611987    320013504    321419125    322828856    324242703    325660672    327082769    328509000    329939371    331373888    332812557    334255384    335702375    337153536    338608873    340068392    341532099    343000000    344472101    345948408    347428927    348913664    350402625    351895816    353393243    354894912    356400829    357911000    359425431    360944128    362467097    363994344    365525875    367061696    368601813    370146232    371694959    373248000    374805361    376367048    377933067    379503424    381078125    382657176    384240583    385828352    387420489    389017000    390617891    392223168    393832837    395446904    397065375    398688256    400315553    401947272    403583419    405224000    406869021    408518488    410172407    411830784    413493625    415160936    416832723    418508992    420189749    421875000    423564751    425259008    426957777    428661064    430368875    432081216    433798093    435519512    437245479    438976000    440711081    442450728    444194947    445943744    447697125    449455096    451217663    452984832    454756609    456533000    458314011    460099648    461889917    463684824    465484375    467288576    469097433    470910952    472729139    474552000    476379541    478211768    480048687    481890304    483736625    485587656    487443403    489303872    491169069    493039000    494913671    496793088    498677257    500566184    502459875    504358336    506261573    508169592    510082399    512000000    513922401    515849608    517781627    519718464    521660125    523606616    525557943    527514112    529475129    531441000    533411731    535387328    537367797    539353144    541343375    543338496    545338513    547343432    549353259    551368000    553387661    555412248    557441767    559476224    561515625    563559976    565609283    567663552    569722789    571787000    573856191    575930368    578009537    580093704    582182875    584277056    586376253    588480472    590589719    592704000    594823321    596947688    599077107    601211584    603351125    605495736    607645423    609800192    611960049    614125000    616295051    618470208    620650477    622835864    625026375    627222016    629422793    631628712    633839779    636056000    638277381    640503928    642735647    644972544    647214625    649461896    651714363    653972032    656234909    658503000    660776311    663054848    665338617    667627624    669921875    672221376    674526133    676836152    679151439    681472000    683797841    686128968    688465387    690807104    693154125    695506456    697864103    700227072    702595369    704969000    707347971    709732288    712121957    714516984    716917375    719323136    721734273    724150792    726572699    729000000    731432701    733870808    736314327    738763264    741217625    743677416    746142643    748613312    751089429    753571000    756058031    758550528    761048497    763551944    766060875    768575296    771095213    773620632    776151559    778688000    781229961    783777448    786330467    788889024    791453125    794022776    796597983    799178752    801765089    804357000    806954491    809557568    812166237    814780504    817400375    820025856    822656953    825293672    827936019    830584000    833237621    835896888    838561807    841232384    843908625    846590536    849278123    851971392    854670349    857375000    860085351    862801408    865523177    868250664    870983875    873722816    876467493    879217912    881974079    884736000    887503681    890277128    893056347    895841344    898632125    901428696    904231063    907039232    909853209    912673000    915498611    918330048    921167317    924010424    926859375    929714176    932574833    935441352    938313739    941192000    944076141    946966168    949862087    952763904    955671625    958585256    961504803    964430272    967361669    970299000    973242271    976191488    979146657    982107784    985074875    988047936    991026973    994011992    997002999     1000000000

$$\cos{\left(x \right)} + \frac{\cos{\left(2 x \right)}}{8} + \frac{\cos{\left(3 x \right)}}{27} + \frac{\cos{\left(4 x \right)}}{64} + \frac{\cos{\left(5 x \right)}}{125} + \frac{\cos{\left(6 x \right)}}{216} + \frac{\cos{\left(7 x \right)}}{343} + \frac{\cos{\left(8 x \right)}}{512} + \frac{\cos{\left(9 x \right)}}{729} + \frac{\cos{\left(10 x \right)}}{1000} + \frac{\cos{\left(11 x \right)}}{1331} + \frac{\cos{\left(12 x \right)}}{1728} + \frac{\cos{\left(13 x \right)}}{2197} + \frac{\cos{\left(14 x \right)}}{2744} + \frac{\cos{\left(15 x \right)}}{3375} + \frac{\cos{\left(16 x \right)}}{4096} + \frac{\cos{\left(17 x \right)}}{4913} + \frac{\cos{\left(18 x \right)}}{5832} + \frac{\cos{\left(19 x \right)}}{6859} + \frac{\cos{\left(20 x \right)}}{8000} + \frac{\cos{\left(21 x \right)}}{9261} + \frac{\cos{\left(22 x \right)}}{10648} + \frac{\cos{\left(23 x \right)}}{12167} + \frac{\cos{\left(24 x \right)}}{13824} + \frac{\cos{\left(25 x \right)}}{15625} + \frac{\cos{\left(26 x \right)}}{17576} + \frac{\cos{\left(27 x \right)}}{19683} + \frac{\cos{\left(28 x \right)}}{21952} + \frac{\cos{\left(29 x \right)}}{24389} + \frac{\cos{\left(30 x \right)}}{27000} + \frac{\cos{\left(31 x \right)}}{29791} + \frac{\cos{\left(32 x \right)}}{32768} + \frac{\cos{\left(33 x \right)}}{35937} + \frac{\cos{\left(34 x \right)}}{39304} + \frac{\cos{\left(35 x \right)}}{42875} + \frac{\cos{\left(36 x \right)}}{46656} + \frac{\cos{\left(37 x \right)}}{50653} + \frac{\cos{\left(38 x \right)}}{54872} + \frac{\cos{\left(39 x \right)}}{59319} + \frac{\cos{\left(40 x \right)}}{64000} + \frac{\cos{\left(41 x \right)}}{68921} + \frac{\cos{\left(42 x \right)}}{74088} + \frac{\cos{\left(43 x \right)}}{79507} + \frac{\cos{\left(44 x \right)}}{85184} + \frac{\cos{\left(45 x \right)}}{91125} + \frac{\cos{\left(46 x \right)}}{97336} + \frac{\cos{\left(47 x \right)}}{103823} + \frac{\cos{\left(48 x \right)}}{110592} + \frac{\cos{\left(49 x \right)}}{117649} + \frac{\cos{\left(50 x \right)}}{125000} + \frac{\cos{\left(51 x \right)}}{132651} + \frac{\cos{\left(52 x \right)}}{140608} + \frac{\cos{\left(53 x \right)}}{148877} + \frac{\cos{\left(54 x \right)}}{157464} + \frac{\cos{\left(55 x \right)}}{166375} + \frac{\cos{\left(56 x \right)}}{175616} + \frac{\cos{\left(57 x \right)}}{185193} + \frac{\cos{\left(58 x \right)}}{195112} + \frac{\cos{\left(59 x \right)}}{205379} + \frac{\cos{\left(60 x \right)}}{216000} + \frac{\cos{\left(61 x \right)}}{226981} + \frac{\cos{\left(62 x \right)}}{238328} + \frac{\cos{\left(63 x \right)}}{250047} + \frac{\cos{\left(64 x \right)}}{262144} + \frac{\cos{\left(65 x \right)}}{274625} + \frac{\cos{\left(66 x \right)}}{287496} + \frac{\cos{\left(67 x \right)}}{300763} + \frac{\cos{\left(68 x \right)}}{314432} + \frac{\cos{\left(69 x \right)}}{328509} + \frac{\cos{\left(70 x \right)}}{343000} + \frac{\cos{\left(71 x \right)}}{357911} + \frac{\cos{\left(72 x \right)}}{373248} + \frac{\cos{\left(73 x \right)}}{389017} + \frac{\cos{\left(74 x \right)}}{405224} + \frac{\cos{\left(75 x \right)}}{421875} + \frac{\cos{\left(76 x \right)}}{438976} + \frac{\cos{\left(77 x \right)}}{456533} + \frac{\cos{\left(78 x \right)}}{474552} + \frac{\cos{\left(79 x \right)}}{493039} + \frac{\cos{\left(80 x \right)}}{512000} + \frac{\cos{\left(81 x \right)}}{531441} + \frac{\cos{\left(82 x \right)}}{551368} + \frac{\cos{\left(83 x \right)}}{571787} + \frac{\cos{\left(84 x \right)}}{592704} + \frac{\cos{\left(85 x \right)}}{614125} + \frac{\cos{\left(86 x \right)}}{636056} + \frac{\cos{\left(87 x \right)}}{658503} + \frac{\cos{\left(88 x \right)}}{681472} + \frac{\cos{\left(89 x \right)}}{704969} + \frac{\cos{\left(90 x \right)}}{729000} + \frac{\cos{\left(91 x \right)}}{753571} + \frac{\cos{\left(92 x \right)}}{778688} + \frac{\cos{\left(93 x \right)}}{804357} + \frac{\cos{\left(94 x \right)}}{830584} + \frac{\cos{\left(95 x \right)}}{857375} + \frac{\cos{\left(96 x \right)}}{884736} + \frac{\cos{\left(97 x 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\right)}}{686128968} + \frac{\cos{\left(883 x \right)}}{688465387} + \frac{\cos{\left(884 x \right)}}{690807104} + \frac{\cos{\left(885 x \right)}}{693154125} + \frac{\cos{\left(886 x \right)}}{695506456} + \frac{\cos{\left(887 x \right)}}{697864103} + \frac{\cos{\left(888 x \right)}}{700227072} + \frac{\cos{\left(889 x \right)}}{702595369} + \frac{\cos{\left(890 x \right)}}{704969000} + \frac{\cos{\left(891 x \right)}}{707347971} + \frac{\cos{\left(892 x \right)}}{709732288} + \frac{\cos{\left(893 x \right)}}{712121957} + \frac{\cos{\left(894 x \right)}}{714516984} + \frac{\cos{\left(895 x \right)}}{716917375} + \frac{\cos{\left(896 x \right)}}{719323136} + \frac{\cos{\left(897 x \right)}}{721734273} + \frac{\cos{\left(898 x \right)}}{724150792} + \frac{\cos{\left(899 x \right)}}{726572699} + \frac{\cos{\left(900 x \right)}}{729000000} + \frac{\cos{\left(901 x \right)}}{731432701} + \frac{\cos{\left(902 x \right)}}{733870808} + \frac{\cos{\left(903 x \right)}}{736314327} + \frac{\cos{\left(904 x \right)}}{738763264} + \frac{\cos{\left(905 x \right)}}{741217625} + \frac{\cos{\left(906 x \right)}}{743677416} + \frac{\cos{\left(907 x \right)}}{746142643} + \frac{\cos{\left(908 x \right)}}{748613312} + \frac{\cos{\left(909 x \right)}}{751089429} + \frac{\cos{\left(910 x \right)}}{753571000} + \frac{\cos{\left(911 x \right)}}{756058031} + \frac{\cos{\left(912 x \right)}}{758550528} + \frac{\cos{\left(913 x \right)}}{761048497} + \frac{\cos{\left(914 x \right)}}{763551944} + \frac{\cos{\left(915 x \right)}}{766060875} + \frac{\cos{\left(916 x \right)}}{768575296} + \frac{\cos{\left(917 x \right)}}{771095213} + \frac{\cos{\left(918 x \right)}}{773620632} + \frac{\cos{\left(919 x \right)}}{776151559} + \frac{\cos{\left(920 x \right)}}{778688000} + \frac{\cos{\left(921 x \right)}}{781229961} + \frac{\cos{\left(922 x \right)}}{783777448} + \frac{\cos{\left(923 x \right)}}{786330467} + \frac{\cos{\left(924 x \right)}}{788889024} + \frac{\cos{\left(925 x \right)}}{791453125} + \frac{\cos{\left(926 x \right)}}{794022776} + \frac{\cos{\left(927 x \right)}}{796597983} + \frac{\cos{\left(928 x \right)}}{799178752} + \frac{\cos{\left(929 x \right)}}{801765089} + \frac{\cos{\left(930 x \right)}}{804357000} + \frac{\cos{\left(931 x \right)}}{806954491} + \frac{\cos{\left(932 x \right)}}{809557568} + \frac{\cos{\left(933 x \right)}}{812166237} + \frac{\cos{\left(934 x \right)}}{814780504} + \frac{\cos{\left(935 x \right)}}{817400375} + \frac{\cos{\left(936 x \right)}}{820025856} + \frac{\cos{\left(937 x \right)}}{822656953} + \frac{\cos{\left(938 x \right)}}{825293672} + \frac{\cos{\left(939 x \right)}}{827936019} + \frac{\cos{\left(940 x \right)}}{830584000} + \frac{\cos{\left(941 x \right)}}{833237621} + \frac{\cos{\left(942 x \right)}}{835896888} + \frac{\cos{\left(943 x \right)}}{838561807} + \frac{\cos{\left(944 x \right)}}{841232384} + \frac{\cos{\left(945 x \right)}}{843908625} + \frac{\cos{\left(946 x \right)}}{846590536} + \frac{\cos{\left(947 x \right)}}{849278123} + \frac{\cos{\left(948 x \right)}}{851971392} + \frac{\cos{\left(949 x \right)}}{854670349} + \frac{\cos{\left(950 x \right)}}{857375000} + \frac{\cos{\left(951 x \right)}}{860085351} + \frac{\cos{\left(952 x \right)}}{862801408} + \frac{\cos{\left(953 x \right)}}{865523177} + \frac{\cos{\left(954 x \right)}}{868250664} + \frac{\cos{\left(955 x \right)}}{870983875} + \frac{\cos{\left(956 x \right)}}{873722816} + \frac{\cos{\left(957 x \right)}}{876467493} + \frac{\cos{\left(958 x \right)}}{879217912} + \frac{\cos{\left(959 x \right)}}{881974079} + \frac{\cos{\left(960 x \right)}}{884736000} + \frac{\cos{\left(961 x \right)}}{887503681} + \frac{\cos{\left(962 x \right)}}{890277128} + \frac{\cos{\left(963 x \right)}}{893056347} + \frac{\cos{\left(964 x \right)}}{895841344} + \frac{\cos{\left(965 x \right)}}{898632125} + \frac{\cos{\left(966 x \right)}}{901428696} + \frac{\cos{\left(967 x \right)}}{904231063} + \frac{\cos{\left(968 x \right)}}{907039232} + \frac{\cos{\left(969 x \right)}}{909853209} + \frac{\cos{\left(970 x \right)}}{912673000} + \frac{\cos{\left(971 x \right)}}{915498611} + \frac{\cos{\left(972 x \right)}}{918330048} + \frac{\cos{\left(973 x \right)}}{921167317} + \frac{\cos{\left(974 x \right)}}{924010424} + \frac{\cos{\left(975 x \right)}}{926859375} + \frac{\cos{\left(976 x \right)}}{929714176} + \frac{\cos{\left(977 x \right)}}{932574833} + \frac{\cos{\left(978 x \right)}}{935441352} + \frac{\cos{\left(979 x \right)}}{938313739} + \frac{\cos{\left(980 x \right)}}{941192000} + \frac{\cos{\left(981 x \right)}}{944076141} + \frac{\cos{\left(982 x \right)}}{946966168} + \frac{\cos{\left(983 x \right)}}{949862087} + \frac{\cos{\left(984 x \right)}}{952763904} + \frac{\cos{\left(985 x \right)}}{955671625} + \frac{\cos{\left(986 x \right)}}{958585256} + \frac{\cos{\left(987 x \right)}}{961504803} + \frac{\cos{\left(988 x \right)}}{964430272} + \frac{\cos{\left(989 x \right)}}{967361669} + \frac{\cos{\left(990 x \right)}}{970299000} + \frac{\cos{\left(991 x \right)}}{973242271} + \frac{\cos{\left(992 x \right)}}{976191488} + \frac{\cos{\left(993 x \right)}}{979146657} + \frac{\cos{\left(994 x \right)}}{982107784} + \frac{\cos{\left(995 x \right)}}{985074875} + \frac{\cos{\left(996 x \right)}}{988047936} + \frac{\cos{\left(997 x \right)}}{991026973} + \frac{\cos{\left(998 x \right)}}{994011992} + \frac{\cos{\left(999 x \right)}}{997002999} + \frac{\cos{\left(1000 x \right)}}{1000000000}$$

cos(2*x)/8 + cos(3*x)/27 + cos(4*x)/64 + cos(5*x)/125 + cos(6*x)/216 + cos(7*x)/343 + cos(8*x)/512 + cos(9*x)/729 + cos(10*x)/1000 + cos(11*x)/1331 + cos(12*x)/1728 + cos(13*x)/2197 + cos(14*x)/2744 + cos(15*x)/3375 + cos(16*x)/4096 + cos(17*x)/4913 + cos(18*x)/5832 + cos(19*x)/6859 + cos(20*x)/8000 + cos(21*x)/9261 + cos(22*x)/10648 + cos(23*x)/12167 + cos(24*x)/13824 + cos(25*x)/15625 + cos(26*x)/17576 + cos(27*x)/19683 + cos(28*x)/21952 + cos(29*x)/24389 + cos(30*x)/27000 + cos(31*x)/29791 + cos(32*x)/32768 + cos(33*x)/35937 + cos(34*x)/39304 + cos(35*x)/42875 + cos(36*x)/46656 + cos(37*x)/50653 + cos(38*x)/54872 + cos(39*x)/59319 + cos(40*x)/64000 + cos(41*x)/68921 + cos(42*x)/74088 + cos(43*x)/79507 + cos(44*x)/85184 + cos(45*x)/91125 + cos(46*x)/97336 + cos(47*x)/103823 + cos(48*x)/110592 + cos(49*x)/117649 + cos(50*x)/125000 + cos(51*x)/132651 + cos(52*x)/140608 + cos(53*x)/148877 + cos(54*x)/157464 + cos(55*x)/166375 + cos(56*x)/175616 + cos(57*x)/185193 + cos(58*x)/195112 + cos(59*x)/205379 + cos(60*x)/216000 + cos(61*x)/226981 + cos(62*x)/238328 + cos(63*x)/250047 + cos(64*x)/262144 + cos(65*x)/274625 + cos(66*x)/287496 + cos(67*x)/300763 + cos(68*x)/314432 + cos(69*x)/328509 + cos(70*x)/343000 + cos(71*x)/357911 + cos(72*x)/373248 + cos(73*x)/389017 + cos(74*x)/405224 + cos(75*x)/421875 + cos(76*x)/438976 + cos(77*x)/456533 + cos(78*x)/474552 + cos(79*x)/493039 + cos(80*x)/512000 + cos(81*x)/531441 + cos(82*x)/551368 + cos(83*x)/571787 + cos(84*x)/592704 + cos(85*x)/614125 + cos(86*x)/636056 + cos(87*x)/658503 + cos(88*x)/681472 + cos(89*x)/704969 + cos(90*x)/729000 + cos(91*x)/753571 + cos(92*x)/778688 + cos(93*x)/804357 + cos(94*x)/830584 + cos(95*x)/857375 + cos(96*x)/884736 + cos(97*x)/912673 + cos(98*x)/941192 + cos(99*x)/970299 + cos(100*x)/1000000 + cos(101*x)/1030301 + cos(102*x)/1061208 + cos(103*x)/1092727 + cos(104*x)/1124864 + cos(105*x)/1157625 + cos(106*x)/1191016 + cos(107*x)/1225043 + cos(108*x)/1259712 + cos(109*x)/1295029 + cos(110*x)/1331000 + cos(111*x)/1367631 + cos(112*x)/1404928 + cos(113*x)/1442897 + cos(114*x)/1481544 + cos(115*x)/1520875 + cos(116*x)/1560896 + cos(117*x)/1601613 + cos(118*x)/1643032 + cos(119*x)/1685159 + cos(120*x)/1728000 + cos(121*x)/1771561 + cos(122*x)/1815848 + cos(123*x)/1860867 + cos(124*x)/1906624 + cos(125*x)/1953125 + cos(126*x)/2000376 + cos(127*x)/2048383 + cos(128*x)/2097152 + cos(129*x)/2146689 + cos(130*x)/2197000 + cos(131*x)/2248091 + cos(132*x)/2299968 + cos(133*x)/2352637 + cos(134*x)/2406104 + cos(135*x)/2460375 + cos(136*x)/2515456 + cos(137*x)/2571353 + cos(138*x)/2628072 + cos(139*x)/2685619 + cos(140*x)/2744000 + cos(141*x)/2803221 + cos(142*x)/2863288 + cos(143*x)/2924207 + cos(144*x)/2985984 + cos(145*x)/3048625 + cos(146*x)/3112136 + cos(147*x)/3176523 + cos(148*x)/3241792 + cos(149*x)/3307949 + cos(150*x)/3375000 + cos(151*x)/3442951 + cos(152*x)/3511808 + cos(153*x)/3581577 + cos(154*x)/3652264 + cos(155*x)/3723875 + cos(156*x)/3796416 + cos(157*x)/3869893 + cos(158*x)/3944312 + cos(159*x)/4019679 + cos(160*x)/4096000 + cos(161*x)/4173281 + cos(162*x)/4251528 + cos(163*x)/4330747 + cos(164*x)/4410944 + cos(165*x)/4492125 + cos(166*x)/4574296 + cos(167*x)/4657463 + cos(168*x)/4741632 + cos(169*x)/4826809 + cos(170*x)/4913000 + cos(171*x)/5000211 + cos(172*x)/5088448 + cos(173*x)/5177717 + cos(174*x)/5268024 + cos(175*x)/5359375 + cos(176*x)/5451776 + cos(177*x)/5545233 + cos(178*x)/5639752 + cos(179*x)/5735339 + cos(180*x)/5832000 + cos(181*x)/5929741 + cos(182*x)/6028568 + cos(183*x)/6128487 + cos(184*x)/6229504 + cos(185*x)/6331625 + cos(186*x)/6434856 + cos(187*x)/6539203 + cos(188*x)/6644672 + cos(189*x)/6751269 + cos(190*x)/6859000 + cos(191*x)/6967871 + cos(192*x)/7077888 + cos(193*x)/7189057 + cos(194*x)/7301384 + cos(195*x)/7414875 + cos(196*x)/7529536 + cos(197*x)/7645373 + cos(198*x)/7762392 + cos(199*x)/7880599 + cos(200*x)/8000000 + cos(201*x)/8120601 + cos(202*x)/8242408 + cos(203*x)/8365427 + cos(204*x)/8489664 + cos(205*x)/8615125 + cos(206*x)/8741816 + cos(207*x)/8869743 + cos(208*x)/8998912 + cos(209*x)/9129329 + cos(210*x)/9261000 + cos(211*x)/9393931 + cos(212*x)/9528128 + cos(213*x)/9663597 + cos(214*x)/9800344 + cos(215*x)/9938375 + cos(216*x)/10077696 + cos(217*x)/10218313 + cos(218*x)/10360232 + cos(219*x)/10503459 + cos(220*x)/10648000 + cos(221*x)/10793861 + cos(222*x)/10941048 + cos(223*x)/11089567 + cos(224*x)/11239424 + cos(225*x)/11390625 + cos(226*x)/11543176 + cos(227*x)/11697083 + cos(228*x)/11852352 + cos(229*x)/12008989 + cos(230*x)/12167000 + cos(231*x)/12326391 + cos(232*x)/12487168 + cos(233*x)/12649337 + cos(234*x)/12812904 + cos(235*x)/12977875 + cos(236*x)/13144256 + cos(237*x)/13312053 + cos(238*x)/13481272 + cos(239*x)/13651919 + cos(240*x)/13824000 + cos(241*x)/13997521 + cos(242*x)/14172488 + cos(243*x)/14348907 + cos(244*x)/14526784 + cos(245*x)/14706125 + cos(246*x)/14886936 + cos(247*x)/15069223 + cos(248*x)/15252992 + cos(249*x)/15438249 + cos(250*x)/15625000 + cos(251*x)/15813251 + cos(252*x)/16003008 + cos(253*x)/16194277 + cos(254*x)/16387064 + cos(255*x)/16581375 + cos(256*x)/16777216 + cos(257*x)/16974593 + cos(258*x)/17173512 + cos(259*x)/17373979 + cos(260*x)/17576000 + cos(261*x)/17779581 + cos(262*x)/17984728 + cos(263*x)/18191447 + cos(264*x)/18399744 + cos(265*x)/18609625 + cos(266*x)/18821096 + cos(267*x)/19034163 + cos(268*x)/19248832 + cos(269*x)/19465109 + cos(270*x)/19683000 + cos(271*x)/19902511 + cos(272*x)/20123648 + cos(273*x)/20346417 + cos(274*x)/20570824 + cos(275*x)/20796875 + cos(276*x)/21024576 + cos(277*x)/21253933 + cos(278*x)/21484952 + cos(279*x)/21717639 + cos(280*x)/21952000 + cos(281*x)/22188041 + cos(282*x)/22425768 + cos(283*x)/22665187 + cos(284*x)/22906304 + cos(285*x)/23149125 + cos(286*x)/23393656 + cos(287*x)/23639903 + cos(288*x)/23887872 + cos(289*x)/24137569 + cos(290*x)/24389000 + cos(291*x)/24642171 + cos(292*x)/24897088 + cos(293*x)/25153757 + cos(294*x)/25412184 + cos(295*x)/25672375 + cos(296*x)/25934336 + cos(297*x)/26198073 + cos(298*x)/26463592 + cos(299*x)/26730899 + cos(300*x)/27000000 + cos(301*x)/27270901 + cos(302*x)/27543608 + cos(303*x)/27818127 + cos(304*x)/28094464 + cos(305*x)/28372625 + cos(306*x)/28652616 + cos(307*x)/28934443 + cos(308*x)/29218112 + cos(309*x)/29503629 + cos(310*x)/29791000 + cos(311*x)/30080231 + cos(312*x)/30371328 + cos(313*x)/30664297 + cos(314*x)/30959144 + cos(315*x)/31255875 + cos(316*x)/31554496 + cos(317*x)/31855013 + cos(318*x)/32157432 + cos(319*x)/32461759 + cos(320*x)/32768000 + cos(321*x)/33076161 + cos(322*x)/33386248 + cos(323*x)/33698267 + cos(324*x)/34012224 + cos(325*x)/34328125 + cos(326*x)/34645976 + cos(327*x)/34965783 + cos(328*x)/35287552 + cos(329*x)/35611289 + cos(330*x)/35937000 + cos(331*x)/36264691 + cos(332*x)/36594368 + cos(333*x)/36926037 + cos(334*x)/37259704 + cos(335*x)/37595375 + cos(336*x)/37933056 + cos(337*x)/38272753 + cos(338*x)/38614472 + cos(339*x)/38958219 + cos(340*x)/39304000 + cos(341*x)/39651821 + cos(342*x)/40001688 + cos(343*x)/40353607 + cos(344*x)/40707584 + cos(345*x)/41063625 + cos(346*x)/41421736 + cos(347*x)/41781923 + cos(348*x)/42144192 + cos(349*x)/42508549 + cos(350*x)/42875000 + cos(351*x)/43243551 + cos(352*x)/43614208 + cos(353*x)/43986977 + cos(354*x)/44361864 + cos(355*x)/44738875 + cos(356*x)/45118016 + cos(357*x)/45499293 + cos(358*x)/45882712 + cos(359*x)/46268279 + cos(360*x)/46656000 + cos(361*x)/47045881 + cos(362*x)/47437928 + cos(363*x)/47832147 + cos(364*x)/48228544 + cos(365*x)/48627125 + cos(366*x)/49027896 + cos(367*x)/49430863 + cos(368*x)/49836032 + cos(369*x)/50243409 + cos(370*x)/50653000 + cos(371*x)/51064811 + cos(372*x)/51478848 + cos(373*x)/51895117 + cos(374*x)/52313624 + cos(375*x)/52734375 + cos(376*x)/53157376 + cos(377*x)/53582633 + cos(378*x)/54010152 + cos(379*x)/54439939 + cos(380*x)/54872000 + cos(381*x)/55306341 + cos(382*x)/55742968 + cos(383*x)/56181887 + cos(384*x)/56623104 + cos(385*x)/57066625 + cos(386*x)/57512456 + cos(387*x)/57960603 + cos(388*x)/58411072 + cos(389*x)/58863869 + cos(390*x)/59319000 + cos(391*x)/59776471 + cos(392*x)/60236288 + cos(393*x)/60698457 + cos(394*x)/61162984 + cos(395*x)/61629875 + cos(396*x)/62099136 + cos(397*x)/62570773 + cos(398*x)/63044792 + cos(399*x)/63521199 + cos(400*x)/64000000 + cos(401*x)/64481201 + cos(402*x)/64964808 + cos(403*x)/65450827 + cos(404*x)/65939264 + cos(405*x)/66430125 + cos(406*x)/66923416 + cos(407*x)/67419143 + cos(408*x)/67917312 + cos(409*x)/68417929 + cos(410*x)/68921000 + cos(411*x)/69426531 + cos(412*x)/69934528 + cos(413*x)/70444997 + cos(414*x)/70957944 + cos(415*x)/71473375 + cos(416*x)/71991296 + cos(417*x)/72511713 + cos(418*x)/73034632 + cos(419*x)/73560059 + cos(420*x)/74088000 + cos(421*x)/74618461 + cos(422*x)/75151448 + cos(423*x)/75686967 + cos(424*x)/76225024 + cos(425*x)/76765625 + cos(426*x)/77308776 + cos(427*x)/77854483 + cos(428*x)/78402752 + cos(429*x)/78953589 + cos(430*x)/79507000 + cos(431*x)/80062991 + cos(432*x)/80621568 + cos(433*x)/81182737 + cos(434*x)/81746504 + cos(435*x)/82312875 + cos(436*x)/82881856 + cos(437*x)/83453453 + cos(438*x)/84027672 + cos(439*x)/84604519 + cos(440*x)/85184000 + cos(441*x)/85766121 + cos(442*x)/86350888 + cos(443*x)/86938307 + cos(444*x)/87528384 + cos(445*x)/88121125 + cos(446*x)/88716536 + cos(447*x)/89314623 + cos(448*x)/89915392 + cos(449*x)/90518849 + cos(450*x)/91125000 + cos(451*x)/91733851 + cos(452*x)/92345408 + cos(453*x)/92959677 + cos(454*x)/93576664 + cos(455*x)/94196375 + cos(456*x)/94818816 + cos(457*x)/95443993 + cos(458*x)/96071912 + cos(459*x)/96702579 + cos(460*x)/97336000 + cos(461*x)/97972181 + cos(462*x)/98611128 + cos(463*x)/99252847 + cos(464*x)/99897344 + cos(465*x)/100544625 + cos(466*x)/101194696 + cos(467*x)/101847563 + cos(468*x)/102503232 + cos(469*x)/103161709 + cos(470*x)/103823000 + cos(471*x)/104487111 + cos(472*x)/105154048 + cos(473*x)/105823817 + cos(474*x)/106496424 + cos(475*x)/107171875 + cos(476*x)/107850176 + cos(477*x)/108531333 + cos(478*x)/109215352 + cos(479*x)/109902239 + cos(480*x)/110592000 + cos(481*x)/111284641 + cos(482*x)/111980168 + cos(483*x)/112678587 + cos(484*x)/113379904 + cos(485*x)/114084125 + cos(486*x)/114791256 + cos(487*x)/115501303 + cos(488*x)/116214272 + cos(489*x)/116930169 + cos(490*x)/117649000 + cos(491*x)/118370771 + cos(492*x)/119095488 + cos(493*x)/119823157 + cos(494*x)/120553784 + cos(495*x)/121287375 + cos(496*x)/122023936 + cos(497*x)/122763473 + cos(498*x)/123505992 + cos(499*x)/124251499 + cos(500*x)/125000000 + cos(501*x)/125751501 + cos(502*x)/126506008 + cos(503*x)/127263527 + cos(504*x)/128024064 + cos(505*x)/128787625 + cos(506*x)/129554216 + cos(507*x)/130323843 + cos(508*x)/131096512 + cos(509*x)/131872229 + cos(510*x)/132651000 + cos(511*x)/133432831 + cos(512*x)/134217728 + cos(513*x)/135005697 + cos(514*x)/135796744 + cos(515*x)/136590875 + cos(516*x)/137388096 + cos(517*x)/138188413 + cos(518*x)/138991832 + cos(519*x)/139798359 + cos(520*x)/140608000 + cos(521*x)/141420761 + cos(522*x)/142236648 + cos(523*x)/143055667 + cos(524*x)/143877824 + cos(525*x)/144703125 + cos(526*x)/145531576 + cos(527*x)/146363183 + cos(528*x)/147197952 + cos(529*x)/148035889 + cos(530*x)/148877000 + cos(531*x)/149721291 + cos(532*x)/150568768 + cos(533*x)/151419437 + cos(534*x)/152273304 + cos(535*x)/153130375 + cos(536*x)/153990656 + cos(537*x)/154854153 + cos(538*x)/155720872 + cos(539*x)/156590819 + cos(540*x)/157464000 + cos(541*x)/158340421 + cos(542*x)/159220088 + cos(543*x)/160103007 + cos(544*x)/160989184 + cos(545*x)/161878625 + cos(546*x)/162771336 + cos(547*x)/163667323 + cos(548*x)/164566592 + cos(549*x)/165469149 + cos(550*x)/166375000 + cos(551*x)/167284151 + cos(552*x)/168196608 + cos(553*x)/169112377 + cos(554*x)/170031464 + cos(555*x)/170953875 + cos(556*x)/171879616 + cos(557*x)/172808693 + cos(558*x)/173741112 + cos(559*x)/174676879 + cos(560*x)/175616000 + cos(561*x)/176558481 + cos(562*x)/177504328 + cos(563*x)/178453547 + cos(564*x)/179406144 + cos(565*x)/180362125 + cos(566*x)/181321496 + cos(567*x)/182284263 + cos(568*x)/183250432 + cos(569*x)/184220009 + cos(570*x)/185193000 + cos(571*x)/186169411 + cos(572*x)/187149248 + cos(573*x)/188132517 + cos(574*x)/189119224 + cos(575*x)/190109375 + cos(576*x)/191102976 + cos(577*x)/192100033 + cos(578*x)/193100552 + cos(579*x)/194104539 + cos(580*x)/195112000 + cos(581*x)/196122941 + cos(582*x)/197137368 + cos(583*x)/198155287 + cos(584*x)/199176704 + cos(585*x)/200201625 + cos(586*x)/201230056 + cos(587*x)/202262003 + cos(588*x)/203297472 + cos(589*x)/204336469 + cos(590*x)/205379000 + cos(591*x)/206425071 + cos(592*x)/207474688 + cos(593*x)/208527857 + cos(594*x)/209584584 + cos(595*x)/210644875 + cos(596*x)/211708736 + cos(597*x)/212776173 + cos(598*x)/213847192 + cos(599*x)/214921799 + cos(600*x)/216000000 + cos(601*x)/217081801 + cos(602*x)/218167208 + cos(603*x)/219256227 + cos(604*x)/220348864 + cos(605*x)/221445125 + cos(606*x)/222545016 + cos(607*x)/223648543 + cos(608*x)/224755712 + cos(609*x)/225866529 + cos(610*x)/226981000 + cos(611*x)/228099131 + cos(612*x)/229220928 + cos(613*x)/230346397 + cos(614*x)/231475544 + cos(615*x)/232608375 + cos(616*x)/233744896 + cos(617*x)/234885113 + cos(618*x)/236029032 + cos(619*x)/237176659 + cos(620*x)/238328000 + cos(621*x)/239483061 + cos(622*x)/240641848 + cos(623*x)/241804367 + cos(624*x)/242970624 + cos(625*x)/244140625 + cos(626*x)/245314376 + cos(627*x)/246491883 + cos(628*x)/247673152 + cos(629*x)/248858189 + cos(630*x)/250047000 + cos(631*x)/251239591 + cos(632*x)/252435968 + cos(633*x)/253636137 + cos(634*x)/254840104 + cos(635*x)/256047875 + cos(636*x)/257259456 + cos(637*x)/258474853 + cos(638*x)/259694072 + cos(639*x)/260917119 + cos(640*x)/262144000 + cos(641*x)/263374721 + cos(642*x)/264609288 + cos(643*x)/265847707 + cos(644*x)/267089984 + cos(645*x)/268336125 + cos(646*x)/269586136 + cos(647*x)/270840023 + cos(648*x)/272097792 + cos(649*x)/273359449 + cos(650*x)/274625000 + cos(651*x)/275894451 + cos(652*x)/277167808 + cos(653*x)/278445077 + cos(654*x)/279726264 + cos(655*x)/281011375 + cos(656*x)/282300416 + cos(657*x)/283593393 + cos(658*x)/284890312 + cos(659*x)/286191179 + cos(660*x)/287496000 + cos(661*x)/288804781 + cos(662*x)/290117528 + cos(663*x)/291434247 + cos(664*x)/292754944 + cos(665*x)/294079625 + cos(666*x)/295408296 + cos(667*x)/296740963 + cos(668*x)/298077632 + cos(669*x)/299418309 + cos(670*x)/300763000 + cos(671*x)/302111711 + cos(672*x)/303464448 + cos(673*x)/304821217 + cos(674*x)/306182024 + cos(675*x)/307546875 + cos(676*x)/308915776 + cos(677*x)/310288733 + cos(678*x)/311665752 + cos(679*x)/313046839 + cos(680*x)/314432000 + cos(681*x)/315821241 + cos(682*x)/317214568 + cos(683*x)/318611987 + cos(684*x)/320013504 + cos(685*x)/321419125 + cos(686*x)/322828856 + cos(687*x)/324242703 + cos(688*x)/325660672 + cos(689*x)/327082769 + cos(690*x)/328509000 + cos(691*x)/329939371 + cos(692*x)/331373888 + cos(693*x)/332812557 + cos(694*x)/334255384 + cos(695*x)/335702375 + cos(696*x)/337153536 + cos(697*x)/338608873 + cos(698*x)/340068392 + cos(699*x)/341532099 + cos(700*x)/343000000 + cos(701*x)/344472101 + cos(702*x)/345948408 + cos(703*x)/347428927 + cos(704*x)/348913664 + cos(705*x)/350402625 + cos(706*x)/351895816 + cos(707*x)/353393243 + cos(708*x)/354894912 + cos(709*x)/356400829 + cos(710*x)/357911000 + cos(711*x)/359425431 + cos(712*x)/360944128 + cos(713*x)/362467097 + cos(714*x)/363994344 + cos(715*x)/365525875 + cos(716*x)/367061696 + cos(717*x)/368601813 + cos(718*x)/370146232 + cos(719*x)/371694959 + cos(720*x)/373248000 + cos(721*x)/374805361 + cos(722*x)/376367048 + cos(723*x)/377933067 + cos(724*x)/379503424 + cos(725*x)/381078125 + cos(726*x)/382657176 + cos(727*x)/384240583 + cos(728*x)/385828352 + cos(729*x)/387420489 + cos(730*x)/389017000 + cos(731*x)/390617891 + cos(732*x)/392223168 + cos(733*x)/393832837 + cos(734*x)/395446904 + cos(735*x)/397065375 + cos(736*x)/398688256 + cos(737*x)/400315553 + cos(738*x)/401947272 + cos(739*x)/403583419 + cos(740*x)/405224000 + cos(741*x)/406869021 + cos(742*x)/408518488 + cos(743*x)/410172407 + cos(744*x)/411830784 + cos(745*x)/413493625 + cos(746*x)/415160936 + cos(747*x)/416832723 + cos(748*x)/418508992 + cos(749*x)/420189749 + cos(750*x)/421875000 + cos(751*x)/423564751 + cos(752*x)/425259008 + cos(753*x)/426957777 + cos(754*x)/428661064 + cos(755*x)/430368875 + cos(756*x)/432081216 + cos(757*x)/433798093 + cos(758*x)/435519512 + cos(759*x)/437245479 + cos(760*x)/438976000 + cos(761*x)/440711081 + cos(762*x)/442450728 + cos(763*x)/444194947 + cos(764*x)/445943744 + cos(765*x)/447697125 + cos(766*x)/449455096 + cos(767*x)/451217663 + cos(768*x)/452984832 + cos(769*x)/454756609 + cos(770*x)/456533000 + cos(771*x)/458314011 + cos(772*x)/460099648 + cos(773*x)/461889917 + cos(774*x)/463684824 + cos(775*x)/465484375 + cos(776*x)/467288576 + cos(777*x)/469097433 + cos(778*x)/470910952 + cos(779*x)/472729139 + cos(780*x)/474552000 + cos(781*x)/476379541 + cos(782*x)/478211768 + cos(783*x)/480048687 + cos(784*x)/481890304 + cos(785*x)/483736625 + cos(786*x)/485587656 + cos(787*x)/487443403 + cos(788*x)/489303872 + cos(789*x)/491169069 + cos(790*x)/493039000 + cos(791*x)/494913671 + cos(792*x)/496793088 + cos(793*x)/498677257 + cos(794*x)/500566184 + cos(795*x)/502459875 + cos(796*x)/504358336 + cos(797*x)/506261573 + cos(798*x)/508169592 + cos(799*x)/510082399 + cos(800*x)/512000000 + cos(801*x)/513922401 + cos(802*x)/515849608 + cos(803*x)/517781627 + cos(804*x)/519718464 + cos(805*x)/521660125 + cos(806*x)/523606616 + cos(807*x)/525557943 + cos(808*x)/527514112 + cos(809*x)/529475129 + cos(810*x)/531441000 + cos(811*x)/533411731 + cos(812*x)/535387328 + cos(813*x)/537367797 + cos(814*x)/539353144 + cos(815*x)/541343375 + cos(816*x)/543338496 + cos(817*x)/545338513 + cos(818*x)/547343432 + cos(819*x)/549353259 + cos(820*x)/551368000 + cos(821*x)/553387661 + cos(822*x)/555412248 + cos(823*x)/557441767 + cos(824*x)/559476224 + cos(825*x)/561515625 + cos(826*x)/563559976 + cos(827*x)/565609283 + cos(828*x)/567663552 + cos(829*x)/569722789 + cos(830*x)/571787000 + cos(831*x)/573856191 + cos(832*x)/575930368 + cos(833*x)/578009537 + cos(834*x)/580093704 + cos(835*x)/582182875 + cos(836*x)/584277056 + cos(837*x)/586376253 + cos(838*x)/588480472 + cos(839*x)/590589719 + cos(840*x)/592704000 + cos(841*x)/594823321 + cos(842*x)/596947688 + cos(843*x)/599077107 + cos(844*x)/601211584 + cos(845*x)/603351125 + cos(846*x)/605495736 + cos(847*x)/607645423 + cos(848*x)/609800192 + cos(849*x)/611960049 + cos(850*x)/614125000 + cos(851*x)/616295051 + cos(852*x)/618470208 + cos(853*x)/620650477 + cos(854*x)/622835864 + cos(855*x)/625026375 + cos(856*x)/627222016 + cos(857*x)/629422793 + cos(858*x)/631628712 + cos(859*x)/633839779 + cos(860*x)/636056000 + cos(861*x)/638277381 + cos(862*x)/640503928 + cos(863*x)/642735647 + cos(864*x)/644972544 + cos(865*x)/647214625 + cos(866*x)/649461896 + cos(867*x)/651714363 + cos(868*x)/653972032 + cos(869*x)/656234909 + cos(870*x)/658503000 + cos(871*x)/660776311 + cos(872*x)/663054848 + cos(873*x)/665338617 + cos(874*x)/667627624 + cos(875*x)/669921875 + cos(876*x)/672221376 + cos(877*x)/674526133 + cos(878*x)/676836152 + cos(879*x)/679151439 + cos(880*x)/681472000 + cos(881*x)/683797841 + cos(882*x)/686128968 + cos(883*x)/688465387 + cos(884*x)/690807104 + cos(885*x)/693154125 + cos(886*x)/695506456 + cos(887*x)/697864103 + cos(888*x)/700227072 + cos(889*x)/702595369 + cos(890*x)/704969000 + cos(891*x)/707347971 + cos(892*x)/709732288 + cos(893*x)/712121957 + cos(894*x)/714516984 + cos(895*x)/716917375 + cos(896*x)/719323136 + cos(897*x)/721734273 + cos(898*x)/724150792 + cos(899*x)/726572699 + cos(900*x)/729000000 + cos(901*x)/731432701 + cos(902*x)/733870808 + cos(903*x)/736314327 + cos(904*x)/738763264 + cos(905*x)/741217625 + cos(906*x)/743677416 + cos(907*x)/746142643 + cos(908*x)/748613312 + cos(909*x)/751089429 + cos(910*x)/753571000 + cos(911*x)/756058031 + cos(912*x)/758550528 + cos(913*x)/761048497 + cos(914*x)/763551944 + cos(915*x)/766060875 + cos(916*x)/768575296 + cos(917*x)/771095213 + cos(918*x)/773620632 + cos(919*x)/776151559 + cos(920*x)/778688000 + cos(921*x)/781229961 + cos(922*x)/783777448 + cos(923*x)/786330467 + cos(924*x)/788889024 + cos(925*x)/791453125 + cos(926*x)/794022776 + cos(927*x)/796597983 + cos(928*x)/799178752 + cos(929*x)/801765089 + cos(930*x)/804357000 + cos(931*x)/806954491 + cos(932*x)/809557568 + cos(933*x)/812166237 + cos(934*x)/814780504 + cos(935*x)/817400375 + cos(936*x)/820025856 + cos(937*x)/822656953 + cos(938*x)/825293672 + cos(939*x)/827936019 + cos(940*x)/830584000 + cos(941*x)/833237621 + cos(942*x)/835896888 + cos(943*x)/838561807 + cos(944*x)/841232384 + cos(945*x)/843908625 + cos(946*x)/846590536 + cos(947*x)/849278123 + cos(948*x)/851971392 + cos(949*x)/854670349 + cos(950*x)/857375000 + cos(951*x)/860085351 + cos(952*x)/862801408 + cos(953*x)/865523177 + cos(954*x)/868250664 + cos(955*x)/870983875 + cos(956*x)/873722816 + cos(957*x)/876467493 + cos(958*x)/879217912 + cos(959*x)/881974079 + cos(960*x)/884736000 + cos(961*x)/887503681 + cos(962*x)/890277128 + cos(963*x)/893056347 + cos(964*x)/895841344 + cos(965*x)/898632125 + cos(966*x)/901428696 + cos(967*x)/904231063 + cos(968*x)/907039232 + cos(969*x)/909853209 + cos(970*x)/912673000 + cos(971*x)/915498611 + cos(972*x)/918330048 + cos(973*x)/921167317 + cos(974*x)/924010424 + cos(975*x)/926859375 + cos(976*x)/929714176 + cos(977*x)/932574833 + cos(978*x)/935441352 + cos(979*x)/938313739 + cos(980*x)/941192000 + cos(981*x)/944076141 + cos(982*x)/946966168 + cos(983*x)/949862087 + cos(984*x)/952763904 + cos(985*x)/955671625 + cos(986*x)/958585256 + cos(987*x)/961504803 + cos(988*x)/964430272 + cos(989*x)/967361669 + cos(990*x)/970299000 + cos(991*x)/973242271 + cos(992*x)/976191488 + cos(993*x)/979146657 + cos(994*x)/982107784 + cos(995*x)/985074875 + cos(996*x)/988047936 + cos(997*x)/991026973 + cos(998*x)/994011992 + cos(999*x)/997002999 + cos(1000*x)/1000000000 + cos(x)

Ejemplos de hallazgo de la suma de la serie

Suma de la serie de potencias
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Serie de Flint Hills
```
csc(n)^2/n^3
```
Serie de cuadrados inversos
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Serie armónica
```
1/n
```
Serie de Grandi
```
(-1)^n
```
Serie alternada
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Serie de Newton-Mercator
```
(-1)^(n + 1)/n*x^n
```
Investigar la convergencia de la serie
```
(3*n - 1)/(-5)^n
```

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Expresiones con funciones

Suma de la serie cos(n*x)/n^3

Solución

Ejemplos de hallazgo de la suma de la serie