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Suma de la serie:
1/n
1/n(n+1)
(-1)^n/n^2
1/(2^n)
Expresiones idénticas
(cos(n)+ uno)/n^ cuatro
( coseno de (n) más 1) dividir por n en el grado 4
( coseno de (n) más uno) dividir por n en el grado cuatro
(cos(n)+1)/n4
cosn+1/n4
(cos(n)+1)/n⁴
cosn+1/n^4
(cos(n)+1) dividir por n^4
Expresiones semejantes
(cos(n)-1)/n^4
Expresiones con funciones
Coseno cos
cosn/n
cosnx/n^p
cos(2n)/2^n
cos(pi*n/180)
cos*2*n*x/4*n^2-1

Suma de la serie/ (cos(n)+1)/n^4

Suma de la serie (cos(n)+1)/n^4

Solución

Ha introducido [src]

 100            
____            
\   `           
 \    cos(n) + 1
  \   ----------
  /        4    
 /        n     
/___,           
n = 1

$$\sum_{n=1}^{100} \frac{\cos{\left(n \right)} + 1}{n^{4}}$$

Sum((cos(n) + 1)/n^4, (n, 1, 100))

Velocidad de la convergencia de la serie

Respuesta [src]

25573826396142386290342085161090605911174681467255914627145778745665552097634641872702493017090099058898714117655761558521744330460542451353750530369257541921150449   cos(2)   cos(3)   cos(4)   cos(5)   cos(6)   cos(7)   cos(8)   cos(9)   cos(10)   cos(11)   cos(12)   cos(13)   cos(14)   cos(15)   cos(16)   cos(17)   cos(18)   cos(19)   cos(20)   cos(21)   cos(22)   cos(23)   cos(24)   cos(25)   cos(26)   cos(27)   cos(28)   cos(29)   cos(30)   cos(31)   cos(32)   cos(33)   cos(34)   cos(35)   cos(36)   cos(37)   cos(38)   cos(39)   cos(40)   cos(41)   cos(42)   cos(43)   cos(44)   cos(45)   cos(46)   cos(47)   cos(48)   cos(49)   cos(50)   cos(51)   cos(52)   cos(53)   cos(54)   cos(55)   cos(56)   cos(57)    cos(58)    cos(59)    cos(60)    cos(61)    cos(62)    cos(63)    cos(64)    cos(65)    cos(66)    cos(67)    cos(68)    cos(69)    cos(70)    cos(71)    cos(72)    cos(73)    cos(74)    cos(75)    cos(76)    cos(77)    cos(78)    cos(79)    cos(80)    cos(81)    cos(82)    cos(83)    cos(84)    cos(85)    cos(86)    cos(87)    cos(88)    cos(89)    cos(90)    cos(91)    cos(92)    cos(93)    cos(94)    cos(95)    cos(96)    cos(97)    cos(98)    cos(99)     cos(100)         
-------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + --------- + cos(1)
23628647485754679362502453724413306715830271665835799111783802082359875324118226512340752054131360850633228709217287632834282348313791572956276708209072537600000000     16       81      256      625      1296     2401     4096     6561     10000     14641     20736     28561     38416     50625     65536     83521     104976    130321    160000    194481    234256    279841    331776    390625    456976    531441    614656    707281    810000    923521   1048576   1185921   1336336   1500625   1679616   1874161   2085136   2313441   2560000   2825761   3111696   3418801   3748096   4100625   4477456   4879681   5308416   5764801   6250000   6765201   7311616   7890481   8503056   9150625   9834496   10556001   11316496   12117361   12960000   13845841   14776336   15752961   16777216   17850625   18974736   20151121   21381376   22667121   24010000   25411681   26873856   28398241   29986576   31640625   33362176   35153041   37015056   38950081   40960000   43046721   45212176   47458321   49787136   52200625   54700816   57289761   59969536   62742241   65610000   68574961   71639296   74805201   78074896   81450625   84934656   88529281   92236816   96059601   100000000

$$\frac{\cos{\left(2 \right)}}{16} + \frac{\cos{\left(3 \right)}}{81} + \frac{\cos{\left(4 \right)}}{256} + \frac{\cos{\left(9 \right)}}{6561} + \frac{\cos{\left(10 \right)}}{10000} + \frac{\cos{\left(8 \right)}}{4096} + \frac{\cos{\left(15 \right)}}{50625} + \frac{\cos{\left(16 \right)}}{65536} + \frac{\cos{\left(22 \right)}}{234256} + \frac{\cos{\left(17 \right)}}{83521} + \frac{\cos{\left(21 \right)}}{194481} + \frac{\cos{\left(23 \right)}}{279841} + \frac{\cos{\left(28 \right)}}{614656} + \frac{\cos{\left(29 \right)}}{707281} + \frac{\cos{\left(34 \right)}}{1336336} + \frac{\cos{\left(35 \right)}}{1500625} + \frac{\cos{\left(27 \right)}}{531441} + \frac{\cos{\left(41 \right)}}{2825761} + \frac{\cos{\left(40 \right)}}{2560000} + \frac{\cos{\left(47 \right)}}{4879681} + \frac{\cos{\left(42 \right)}}{3111696} + \frac{\cos{\left(48 \right)}}{5308416} + \frac{\cos{\left(53 \right)}}{7890481} + \frac{\cos{\left(54 \right)}}{8503056} + \frac{\cos{\left(46 \right)}}{4477456} + \frac{\cos{\left(36 \right)}}{1679616} + \frac{\cos{\left(60 \right)}}{12960000} + \frac{\cos{\left(59 \right)}}{12117361} + \frac{\cos{\left(66 \right)}}{18974736} + \frac{\cos{\left(72 \right)}}{26873856} + \frac{\cos{\left(65 \right)}}{17850625} + \frac{\cos{\left(73 \right)}}{28398241} + \frac{\cos{\left(67 \right)}}{20151121} + \frac{\cos{\left(78 \right)}}{37015056} + \frac{\cos{\left(79 \right)}}{38950081} + \frac{\cos{\left(52 \right)}}{7311616} + \frac{\cos{\left(85 \right)}}{52200625} + \frac{\cos{\left(61 \right)}}{13845841} + \frac{\cos{\left(91 \right)}}{68574961} + \frac{\cos{\left(84 \right)}}{49787136} + \frac{\cos{\left(71 \right)}}{25411681} + \frac{\cos{\left(33 \right)}}{1185921} + \frac{\cos{\left(97 \right)}}{88529281} + \frac{\cos{\left(98 \right)}}{92236816} + \frac{\cos{\left(92 \right)}}{71639296} + \frac{\cos{\left(86 \right)}}{54700816} + \frac{\cos{\left(90 \right)}}{65610000} + \frac{\cos{\left(80 \right)}}{40960000} + \frac{\cos{\left(96 \right)}}{84934656} + \frac{\cos{\left(77 \right)}}{35153041} + \frac{\cos{\left(99 \right)}}{96059601} + \frac{\cos{\left(55 \right)}}{9150625} + \frac{\cos{\left(93 \right)}}{74805201} + \frac{\cos{\left(83 \right)}}{47458321} + \frac{\cos{\left(74 \right)}}{29986576} + \frac{\cos{\left(89 \right)}}{62742241} + \frac{\cos{\left(100 \right)}}{100000000} + \frac{\cos{\left(95 \right)}}{81450625} + \frac{\cos{\left(87 \right)}}{57289761} + \frac{\cos{\left(58 \right)}}{11316496} + \frac{\cos{\left(94 \right)}}{78074896} + \frac{\cos{\left(88 \right)}}{59969536} + \frac{\cos{\left(81 \right)}}{43046721} + \frac{\cos{\left(68 \right)}}{21381376} + \frac{\cos{\left(82 \right)}}{45212176} + \frac{\cos{\left(64 \right)}}{16777216} + \frac{\cos{\left(76 \right)}}{33362176} + \frac{\cos{\left(70 \right)}}{24010000} + \frac{\cos{\left(75 \right)}}{31640625} + \frac{\cos{\left(69 \right)}}{22667121} + \frac{\cos{\left(62 \right)}}{14776336} + \frac{\cos{\left(49 \right)}}{5764801} + \frac{\cos{\left(63 \right)}}{15752961} + \frac{\cos{\left(57 \right)}}{10556001} + \frac{\cos{\left(56 \right)}}{9834496} + \frac{\cos{\left(51 \right)}}{6765201} + \frac{\cos{\left(39 \right)}}{2313441} + \frac{\cos{\left(45 \right)}}{4100625} + \frac{\cos{\left(50 \right)}}{6250000} + \frac{\cos{\left(43 \right)}}{3418801} + \frac{\cos{\left(30 \right)}}{810000} + \frac{\cos{\left(44 \right)}}{3748096} + \frac{\cos{\left(11 \right)}}{14641} + \frac{\cos{\left(37 \right)}}{1874161} + \frac{\cos{\left(38 \right)}}{2085136} + \frac{\cos{\left(32 \right)}}{1048576} + \frac{\cos{\left(31 \right)}}{923521} + \frac{\cos{\left(24 \right)}}{331776} + \frac{\cos{\left(26 \right)}}{456976} + \frac{\cos{\left(25 \right)}}{390625} + \frac{\cos{\left(20 \right)}}{160000} + \frac{\cos{\left(14 \right)}}{38416} + \frac{\cos{\left(18 \right)}}{104976} + \frac{\cos{\left(19 \right)}}{130321} + \frac{\cos{\left(13 \right)}}{28561} + \frac{\cos{\left(12 \right)}}{20736} + \frac{\cos{\left(7 \right)}}{2401} + \frac{\cos{\left(5 \right)}}{625} + \frac{\cos{\left(6 \right)}}{1296} + \cos{\left(1 \right)} + \frac{25573826396142386290342085161090605911174681467255914627145778745665552097634641872702493017090099058898714117655761558521744330460542451353750530369257541921150449}{23628647485754679362502453724413306715830271665835799111783802082359875324118226512340752054131360850633228709217287632834282348313791572956276708209072537600000000}$$

25573826396142386290342085161090605911174681467255914627145778745665552097634641872702493017090099058898714117655761558521744330460542451353750530369257541921150449/23628647485754679362502453724413306715830271665835799111783802082359875324118226512340752054131360850633228709217287632834282348313791572956276708209072537600000000 + cos(2)/16 + cos(3)/81 + cos(4)/256 + cos(5)/625 + cos(6)/1296 + cos(7)/2401 + cos(8)/4096 + cos(9)/6561 + cos(10)/10000 + cos(11)/14641 + cos(12)/20736 + cos(13)/28561 + cos(14)/38416 + cos(15)/50625 + cos(16)/65536 + cos(17)/83521 + cos(18)/104976 + cos(19)/130321 + cos(20)/160000 + cos(21)/194481 + cos(22)/234256 + cos(23)/279841 + cos(24)/331776 + cos(25)/390625 + cos(26)/456976 + cos(27)/531441 + cos(28)/614656 + cos(29)/707281 + cos(30)/810000 + cos(31)/923521 + cos(32)/1048576 + cos(33)/1185921 + cos(34)/1336336 + cos(35)/1500625 + cos(36)/1679616 + cos(37)/1874161 + cos(38)/2085136 + cos(39)/2313441 + cos(40)/2560000 + cos(41)/2825761 + cos(42)/3111696 + cos(43)/3418801 + cos(44)/3748096 + cos(45)/4100625 + cos(46)/4477456 + cos(47)/4879681 + cos(48)/5308416 + cos(49)/5764801 + cos(50)/6250000 + cos(51)/6765201 + cos(52)/7311616 + cos(53)/7890481 + cos(54)/8503056 + cos(55)/9150625 + cos(56)/9834496 + cos(57)/10556001 + cos(58)/11316496 + cos(59)/12117361 + cos(60)/12960000 + cos(61)/13845841 + cos(62)/14776336 + cos(63)/15752961 + cos(64)/16777216 + cos(65)/17850625 + cos(66)/18974736 + cos(67)/20151121 + cos(68)/21381376 + cos(69)/22667121 + cos(70)/24010000 + cos(71)/25411681 + cos(72)/26873856 + cos(73)/28398241 + cos(74)/29986576 + cos(75)/31640625 + cos(76)/33362176 + cos(77)/35153041 + cos(78)/37015056 + cos(79)/38950081 + cos(80)/40960000 + cos(81)/43046721 + cos(82)/45212176 + cos(83)/47458321 + cos(84)/49787136 + cos(85)/52200625 + cos(86)/54700816 + cos(87)/57289761 + cos(88)/59969536 + cos(89)/62742241 + cos(90)/65610000 + cos(91)/68574961 + cos(92)/71639296 + cos(93)/74805201 + cos(94)/78074896 + cos(95)/81450625 + cos(96)/84934656 + cos(97)/88529281 + cos(98)/92236816 + cos(99)/96059601 + cos(100)/100000000 + cos(1)

Respuesta numérica [src]

1.58314515941033059121312868279

1.58314515941033059121312868279

Gráfico

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
```

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

Suma de la serie (cos(n)+1)/n^4

Solución

Ejemplos de hallazgo de la suma de la serie