Sr Examen

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Otras calculadoras

¿Cómo usar?
Suma de la serie:
(w+1)/w
n^2/2^n
(1/3)^n
(4x)^(2n)
Expresiones idénticas
cos dos n/n^2
coseno de 2n dividir por n al cuadrado
coseno de dos n dividir por n al cuadrado
cos2n/n2
cos2n/n²
cos2n/n en el grado 2
cos2n dividir por n^2
Expresiones semejantes
(cos2n)/(n^2)

Suma de la serie/ cos2n/n^2

Suma de la serie cos2n/n^2

Solución

Ha introducido [src]

 100          
____          
\   `         
 \    cos(2*n)
  \   --------
  /       2   
 /       n    
/___,         
n = 1

$$\sum_{n=1}^{100} \frac{\cos{\left(2 n \right)}}{n^{2}}$$

Sum(cos(2*n)/n^2, (n, 1, 100))

Velocidad de la convergencia de la serie

Respuesta [src]

cos(4)   cos(6)   cos(8)   cos(10)   cos(12)   cos(14)   cos(16)   cos(18)   cos(20)   cos(22)   cos(24)   cos(26)   cos(28)   cos(30)   cos(32)   cos(34)   cos(36)   cos(38)   cos(40)   cos(42)   cos(44)   cos(46)   cos(48)   cos(50)   cos(52)   cos(54)   cos(56)   cos(58)   cos(60)   cos(62)   cos(64)   cos(66)   cos(68)   cos(70)   cos(72)   cos(74)   cos(76)   cos(78)   cos(80)   cos(82)   cos(84)   cos(86)   cos(88)   cos(90)   cos(92)   cos(94)   cos(96)   cos(98)   cos(100)   cos(102)   cos(104)   cos(106)   cos(108)   cos(110)   cos(112)   cos(114)   cos(116)   cos(118)   cos(120)   cos(122)   cos(124)   cos(126)   cos(128)   cos(130)   cos(132)   cos(134)   cos(136)   cos(138)   cos(140)   cos(142)   cos(144)   cos(146)   cos(148)   cos(150)   cos(152)   cos(154)   cos(156)   cos(158)   cos(160)   cos(162)   cos(164)   cos(166)   cos(168)   cos(170)   cos(172)   cos(174)   cos(176)   cos(178)   cos(180)   cos(182)   cos(184)   cos(186)   cos(188)   cos(190)   cos(192)   cos(194)   cos(196)   cos(198)   cos(200)         
------ + ------ + ------ + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + ------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + -------- + cos(2)
  4        9        16        25        36        49        64        81       100       121       144       169       196       225       256       289       324       361       400       441       484       529       576       625       676       729       784       841       900       961       1024      1089      1156      1225      1296      1369      1444      1521      1600      1681      1764      1849      1936      2025      2116      2209      2304      2401      2500       2601       2704       2809       2916       3025       3136       3249       3364       3481       3600       3721       3844       3969       4096       4225       4356       4489       4624       4761       4900       5041       5184       5329       5476       5625       5776       5929       6084       6241       6400       6561       6724       6889       7056       7225       7396       7569       7744       7921       8100       8281       8464       8649       8836       9025       9216       9409       9604       9801      10000

$$\cos{\left(2 \right)} + \frac{\cos{\left(4 \right)}}{4} + \frac{\cos{\left(10 \right)}}{25} + \frac{\cos{\left(16 \right)}}{64} + \frac{\cos{\left(8 \right)}}{16} + \frac{\cos{\left(22 \right)}}{121} + \frac{\cos{\left(28 \right)}}{196} + \frac{\cos{\left(34 \right)}}{289} + \frac{\cos{\left(40 \right)}}{400} + \frac{\cos{\left(54 \right)}}{729} + \frac{\cos{\left(48 \right)}}{576} + \frac{\cos{\left(60 \right)}}{900} + \frac{\cos{\left(66 \right)}}{1089} + \frac{\cos{\left(42 \right)}}{441} + \frac{\cos{\left(46 \right)}}{529} + \frac{\cos{\left(72 \right)}}{1296} + \frac{\cos{\left(78 \right)}}{1521} + \frac{\cos{\left(36 \right)}}{324} + \frac{\cos{\left(84 \right)}}{1764} + \frac{\cos{\left(104 \right)}}{2704} + \frac{\cos{\left(98 \right)}}{2401} + \frac{\cos{\left(110 \right)}}{3025} + \frac{\cos{\left(92 \right)}}{2116} + \frac{\cos{\left(116 \right)}}{3364} + \frac{\cos{\left(52 \right)}}{676} + \frac{\cos{\left(122 \right)}}{3721} + \frac{\cos{\left(90 \right)}}{2025} + \frac{\cos{\left(86 \right)}}{1849} + \frac{\cos{\left(148 \right)}}{5476} + \frac{\cos{\left(128 \right)}}{4096} + \frac{\cos{\left(154 \right)}}{5929} + \frac{\cos{\left(142 \right)}}{5041} + \frac{\cos{\left(160 \right)}}{6400} + \frac{\cos{\left(136 \right)}}{4624} + \frac{\cos{\left(166 \right)}}{6889} + \frac{\cos{\left(134 \right)}}{4489} + \frac{\cos{\left(198 \right)}}{9801} + \frac{\cos{\left(192 \right)}}{9216} + \frac{\cos{\left(172 \right)}}{7396} + \frac{\cos{\left(186 \right)}}{8649} + \frac{\cos{\left(130 \right)}}{4225} + \frac{\cos{\left(96 \right)}}{2304} + \frac{\cos{\left(180 \right)}}{8100} + \frac{\cos{\left(80 \right)}}{1600} + \frac{\cos{\left(178 \right)}}{7921} + \frac{\cos{\left(174 \right)}}{7569} + \frac{\cos{\left(140 \right)}}{4900} + \frac{\cos{\left(184 \right)}}{8464} + \frac{\cos{\left(124 \right)}}{3844} + \frac{\cos{\left(168 \right)}}{7056} + \frac{\cos{\left(190 \right)}}{9025} + \frac{\cos{\left(146 \right)}}{5329} + \frac{\cos{\left(162 \right)}}{6561} + \frac{\cos{\left(196 \right)}}{9604} + \frac{\cos{\left(102 \right)}}{2601} + \frac{\cos{\left(200 \right)}}{10000} + \frac{\cos{\left(118 \right)}}{3481} + \frac{\cos{\left(152 \right)}}{5776} + \frac{\cos{\left(194 \right)}}{9409} + \frac{\cos{\left(156 \right)}}{6084} + \frac{\cos{\left(158 \right)}}{6241} + \frac{\cos{\left(188 \right)}}{8836} + \frac{\cos{\left(182 \right)}}{8281} + \frac{\cos{\left(164 \right)}}{6724} + \frac{\cos{\left(150 \right)}}{5625} + \frac{\cos{\left(74 \right)}}{1369} + \frac{\cos{\left(108 \right)}}{2916} + \frac{\cos{\left(176 \right)}}{7744} + \frac{\cos{\left(170 \right)}}{7225} + \frac{\cos{\left(58 \right)}}{841} + \frac{\cos{\left(112 \right)}}{3136} + \frac{\cos{\left(144 \right)}}{5184} + \frac{\cos{\left(114 \right)}}{3249} + \frac{\cos{\left(138 \right)}}{4761} + \frac{\cos{\left(120 \right)}}{3600} + \frac{\cos{\left(132 \right)}}{4356} + \frac{\cos{\left(126 \right)}}{3969} + \frac{\cos{\left(106 \right)}}{2809} + \frac{\cos{\left(100 \right)}}{2500} + \frac{\cos{\left(68 \right)}}{1156} + \frac{\cos{\left(64 \right)}}{1024} + \frac{\cos{\left(94 \right)}}{2209} + \frac{\cos{\left(88 \right)}}{1936} + \frac{\cos{\left(70 \right)}}{1225} + \frac{\cos{\left(82 \right)}}{1681} + \frac{\cos{\left(76 \right)}}{1444} + \frac{\cos{\left(30 \right)}}{225} + \frac{\cos{\left(62 \right)}}{961} + \frac{\cos{\left(56 \right)}}{784} + \frac{\cos{\left(50 \right)}}{625} + \frac{\cos{\left(44 \right)}}{484} + \frac{\cos{\left(38 \right)}}{361} + \frac{\cos{\left(14 \right)}}{49} + \frac{\cos{\left(24 \right)}}{144} + \frac{\cos{\left(32 \right)}}{256} + \frac{\cos{\left(26 \right)}}{169} + \frac{\cos{\left(20 \right)}}{100} + \frac{\cos{\left(18 \right)}}{81} + \frac{\cos{\left(12 \right)}}{36} + \frac{\cos{\left(6 \right)}}{9}$$

cos(4)/4 + cos(6)/9 + cos(8)/16 + cos(10)/25 + cos(12)/36 + cos(14)/49 + cos(16)/64 + cos(18)/81 + cos(20)/100 + cos(22)/121 + cos(24)/144 + cos(26)/169 + cos(28)/196 + cos(30)/225 + cos(32)/256 + cos(34)/289 + cos(36)/324 + cos(38)/361 + cos(40)/400 + cos(42)/441 + cos(44)/484 + cos(46)/529 + cos(48)/576 + cos(50)/625 + cos(52)/676 + cos(54)/729 + cos(56)/784 + cos(58)/841 + cos(60)/900 + cos(62)/961 + cos(64)/1024 + cos(66)/1089 + cos(68)/1156 + cos(70)/1225 + cos(72)/1296 + cos(74)/1369 + cos(76)/1444 + cos(78)/1521 + cos(80)/1600 + cos(82)/1681 + cos(84)/1764 + cos(86)/1849 + cos(88)/1936 + cos(90)/2025 + cos(92)/2116 + cos(94)/2209 + cos(96)/2304 + cos(98)/2401 + cos(100)/2500 + cos(102)/2601 + cos(104)/2704 + cos(106)/2809 + cos(108)/2916 + cos(110)/3025 + cos(112)/3136 + cos(114)/3249 + cos(116)/3364 + cos(118)/3481 + cos(120)/3600 + cos(122)/3721 + cos(124)/3844 + cos(126)/3969 + cos(128)/4096 + cos(130)/4225 + cos(132)/4356 + cos(134)/4489 + cos(136)/4624 + cos(138)/4761 + cos(140)/4900 + cos(142)/5041 + cos(144)/5184 + cos(146)/5329 + cos(148)/5476 + cos(150)/5625 + cos(152)/5776 + cos(154)/5929 + cos(156)/6084 + cos(158)/6241 + cos(160)/6400 + cos(162)/6561 + cos(164)/6724 + cos(166)/6889 + cos(168)/7056 + cos(170)/7225 + cos(172)/7396 + cos(174)/7569 + cos(176)/7744 + cos(178)/7921 + cos(180)/8100 + cos(182)/8281 + cos(184)/8464 + cos(186)/8649 + cos(188)/8836 + cos(190)/9025 + cos(192)/9216 + cos(194)/9409 + cos(196)/9604 + cos(198)/9801 + cos(200)/10000 + cos(2)

Respuesta numérica [src]

-0.496662602255437840826797611620

-0.496662602255437840826797611620

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

Suma de la serie cos2n/n^2

Solución

Ejemplos de hallazgo de la suma de la serie