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Suma de la serie:
x^n/n!
(-1)^n/(2n)!
(2^n+3^n)/(6^n)
1/(4^n)
Expresiones idénticas
cos(n*pi/ ciento ochenta)
coseno de (n multiplicar por número pi dividir por 180)
coseno de (n multiplicar por número pi dividir por ciento ochenta)
cos(npi/180)
cosnpi/180
cos(n*pi dividir por 180)
Expresiones con funciones
Coseno cos
cos(n*p)/4
cos(3*pi*n)/(n^3+2)
cos2n/(2^n)
cosn/2^n+1
cose^n/(2*n^2-8)
Número Pi pi
pi/3^(2n+1)/(2n+1)!
pi/2-arctg(n)
pi*sin(pi*i/(2*n))/((2*n))
pi*n*cos(pi*n*(n-1)/2)/2
pi/n

Suma de la serie/ cos(n*pi/180)

Suma de la serie cos(n*pi/180)

Solución

Ha introducido [src]

 140           
 ___           
 \  `          
  \      /n*pi\
   )  cos|----|
  /      \180 /
 /__,          
n = 1

$$\sum_{n=1}^{140} \cos{\left(\frac{\pi n}{180} \right)}$$

Sum(cos((n*pi)/180), (n, 1, 140))

Velocidad de la convergencia de la serie

Respuesta [src]

                                            ___________                   /     ___________                    \ /           ___________                    \   /     ___________                    \ /             ___________                    \   /     ___________                    \ /           ___________                    \   /       ___________                    \ /           ___________                    \   /           ___________                    \ /                       ___________\   /           ___________                    \ /                         ___________\   /           ___________                    \ /                       ___________\   /                               ___________\ /                         ___________\              ___________              ___________                                  ___________              ___________                                                                                                                                                                                                                                                                                                                                                                 
                                           /       ___                    |    /       ___          /      ___\| |          /       ___          /      ___\|   |    /       ___          /      ___\| |            /       ___          /      ___\|   |    /       ___          /      ___\| |          /       ___          /      ___\|   |      /       ___          /      ___\| |          /       ___          /      ___\|   |          /       ___          /      ___\| |                      /       ___ |   |          /       ___          /      ___\| |                        /       ___ |   |          /       ___          /      ___\| |                      /       ___ |   |      /      ___\             /       ___ | |                        /       ___ |             /       ___              /       ___          /      ___\             /       ___              /       ___          /      ___\         /      ___\                                                                                                                                                                                                                                                                                                                         
         ___________                      /  5   \/ 5                     |   /  5   \/ 5       ___ |1   \/ 5 || |  ___    /  5   \/ 5       ___ |1   \/ 5 ||   |   /  5   \/ 5       ___ |1   \/ 5 || |    ___    /  5   \/ 5       ___ |1   \/ 5 ||   |   /  5   \/ 5       ___ |1   \/ 5 || |  ___    /  5   \/ 5       ___ |1   \/ 5 ||   |     /  5   \/ 5       ___ |1   \/ 5 || |  ___    /  5   \/ 5       ___ |1   \/ 5 ||   |  ___    /  5   \/ 5       ___ |1   \/ 5 || |              ___    /  5   \/ 5  |   |  ___    /  5   \/ 5       ___ |1   \/ 5 || |                ___    /  5   \/ 5  |   |  ___    /  5   \/ 5       ___ |1   \/ 5 || |              ___    /  5   \/ 5  |   |  ___ |1   \/ 5 |     ___    /  5   \/ 5  | |                ___    /  5   \/ 5  |     ___    /  5   \/ 5       ___    /  5   \/ 5       ___ |1   \/ 5 |     ___    /  5   \/ 5       ___    /  5   \/ 5       ___ |1   \/ 5 |     ___ |1   \/ 5 |                                                                                                                                                                                                                                                                                                                         
        /       ___      ___     ___     /   - - -----      ___     ___   |  /   - - -----    \/ 3 *|- + -----|| |\/ 2 *  /   - - -----    \/ 2 *|- + -----||   |  /   - + -----    \/ 3 *|- - -----|| |  \/ 2 *  /   - + -----    \/ 2 *|- - -----||   |  /   - + -----    \/ 3 *|- - -----|| |\/ 2 *  /   - + -----    \/ 2 *|- - -----||   |    /   - - -----    \/ 3 *|- + -----|| |\/ 2 *  /   - - -----    \/ 2 *|- + -----||   |\/ 2 *  /   - - -----    \/ 2 *|- + -----|| |      ___   \/ 3 *  /   - - ----- |   |\/ 2 *  /   - + -----    \/ 2 *|- - -----|| |        ___   \/ 3 *  /   - + ----- |   |\/ 2 *  /   - + -----    \/ 2 *|- - -----|| |      ___   \/ 3 *  /   - + ----- |   |\/ 2 *|- + -----|   \/ 2 *  /   - - ----- | |        ___   \/ 3 *  /   - - ----- |   \/ 2 *  /   - - -----    \/ 2 *  /   - + -----    \/ 2 *|- + -----|   \/ 3 *  /   - - -----    \/ 3 *  /   - + -----    \/ 3 *|- + -----|   \/ 2 *|- - -----|                                                                                                                                                                                                                                                                                                                         
1      /  5   \/ 5     \/ 3    \/ 5    \/    8     8      \/ 2    \/ 6    |\/    8     8            \4     4  /| |      \/    8     8            \4     4  /|   |\/    8     8            \4     4  /| |        \/    8     8            \4     4  /|   |\/    8     8            \4     4  /| |      \/    8     8            \4     4  /|   |  \/    8     8            \4     4  /| |      \/    8     8            \4     4  /|   |      \/    8     8            \4     4  /| |1   \/ 5          \/    8     8   |   |      \/    8     8            \4     4  /| |  1   \/ 5          \/    8     8   |   |      \/    8     8            \4     4  /| |1   \/ 5          \/    8     8   |   |      \4     4  /         \/    8     8   | |  1   \/ 5          \/    8     8   |         \/    8     8            \/    8     8            \4     4  /         \/    8     8            \/    8     8            \4     4  /         \4     4  /      /pi\      /pi\      /pi\      /pi\      /pi\      / pi\      /2*pi\      /4*pi\      /5*pi\      /7*pi\      /7*pi\      /7*pi\      /7*pi\      /8*pi\      /11*pi\      /11*pi\      /13*pi\      /13*pi\      /17*pi\      /17*pi\      /19*pi\      /19*pi\      /23*pi\      /29*pi\      /31*pi\      /37*pi\
- +   /   - + -----  + ----- + ----- + ---------------- + ----- + ----- + |---------------- + -----------------|*|---------------------- + -----------------| + |---------------- + -----------------|*|- ---------------------- - -----------------| + |---------------- - -----------------|*|---------------------- + -----------------| + |- ---------------- + -----------------|*|---------------------- - -----------------| + |---------------------- + -----------------|*|- + ----- + ----------------------| + |---------------------- - -----------------|*|- - + ----- + ----------------------| + |---------------------- - -----------------|*|- - ----- + ----------------------| + |----------------- - ----------------------|*|- - - ----- + ----------------------| + ---------------------- + ---------------------- + ----------------- + ---------------------- + ---------------------- + ----------------- - ----------------- + cos|--| + cos|--| + cos|--| + cos|--| + cos|--| + cos|---| + cos|----| + cos|----| + cos|----| + cos|----| + cos|----| + cos|----| + cos|----| + cos|----| + cos|-----| + cos|-----| + cos|-----| + cos|-----| + cos|-----| + cos|-----| + cos|-----| + cos|-----| + cos|-----| + cos|-----| + cos|-----| + cos|-----|
4   \/    8     8        2       2            2             4       4     \       2                   2        / \          2                      2        /   \       2                   2        / \            2                      2        /   \       2                   2        / \          2                      2        /   \         2                   2        / \          2                      2        /   \          2                      2        / \8     8               2           /   \          2                      2        / \  8     8               2           /   \          2                      2        / \8     8               2           /   \        2                     2           / \  8     8               2           /             2                        2                      2                     2                        2                      2                   2              \9 /      \18/      \36/      \45/      \90/      \180/      \ 45 /      \ 45 /      \ 36 /      \ 36 /      \ 45 /      \ 90 /      \180 /      \ 45 /      \  90 /      \ 180 /      \  90 /      \ 180 /      \  90 /      \ 180 /      \  90 /      \ 180 /      \ 180 /      \ 180 /      \ 180 /      \ 180 /

$$\left(- \frac{\sqrt{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{\sqrt{2} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2}\right) \left(\frac{\sqrt{3} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right) + \left(- \frac{\sqrt{2} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right) \left(- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{\sqrt{3} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2}\right) + \left(- \frac{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{\sqrt{2} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2}\right) \left(- \frac{\sqrt{5}}{8} - \frac{1}{8} + \frac{\sqrt{3} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right) - \frac{\sqrt{2} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{1}{4} + \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \left(\frac{\sqrt{2} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right) \left(- \frac{\sqrt{3} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right) + \frac{\sqrt{2}}{4} + \frac{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{\sqrt{3} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{\sqrt{2} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2} + \left(- \frac{\sqrt{2} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right) \left(- \frac{\sqrt{5}}{8} + \frac{1}{8} + \frac{\sqrt{3} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right) + \frac{\sqrt{6}}{4} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} + \frac{\sqrt{3} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2} + \cos{\left(\frac{19 \pi}{90} \right)} + \cos{\left(\frac{37 \pi}{180} \right)} + \cos{\left(\frac{7 \pi}{36} \right)} + \frac{\sqrt{3} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} + \cos{\left(\frac{17 \pi}{90} \right)} + \cos{\left(\frac{8 \pi}{45} \right)} + \cos{\left(\frac{31 \pi}{180} \right)} + \frac{\sqrt{3}}{2} + \left(- \frac{\sqrt{2} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right) \left(- \frac{1}{8} + \frac{\sqrt{5}}{8} + \frac{\sqrt{3} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right) + \cos{\left(\frac{29 \pi}{180} \right)} + \cos{\left(\frac{7 \pi}{45} \right)} + \cos{\left(\frac{13 \pi}{90} \right)} + \left(\frac{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{\sqrt{2} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2}\right) \left(\frac{1}{8} + \frac{\sqrt{5}}{8} + \frac{\sqrt{3} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right) + \cos{\left(\frac{5 \pi}{36} \right)} + \cos{\left(\frac{23 \pi}{180} \right)} + \cos{\left(\frac{11 \pi}{90} \right)} + \cos{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{19 \pi}{180} \right)} + \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} + \cos{\left(\frac{17 \pi}{180} \right)} + \cos{\left(\frac{4 \pi}{45} \right)} + \cos{\left(\frac{7 \pi}{90} \right)} + \cos{\left(\frac{13 \pi}{180} \right)} + \cos{\left(\frac{11 \pi}{180} \right)} + \left(\frac{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{\sqrt{2} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2}\right) \left(\frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{\sqrt{3} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2}\right) + \cos{\left(\frac{\pi}{18} \right)} + \cos{\left(\frac{2 \pi}{45} \right)} + \cos{\left(\frac{7 \pi}{180} \right)} + \cos{\left(\frac{\pi}{36} \right)} + \cos{\left(\frac{\pi}{45} \right)} + \cos{\left(\frac{\pi}{90} \right)} + \cos{\left(\frac{\pi}{180} \right)} + \frac{\sqrt{5}}{2}$$

1/4 + sqrt(5/8 + sqrt(5)/8) + sqrt(3)/2 + sqrt(5)/2 + sqrt(5/8 - sqrt(5)/8)/2 + sqrt(2)/4 + sqrt(6)/4 + (sqrt(5/8 - sqrt(5)/8)/2 + sqrt(3)*(1/4 + sqrt(5)/4)/2)*(sqrt(2)*sqrt(5/8 - sqrt(5)/8)/2 + sqrt(2)*(1/4 + sqrt(5)/4)/2) + (sqrt(5/8 + sqrt(5)/8)/2 + sqrt(3)*(1/4 - sqrt(5)/4)/2)*(-sqrt(2)*sqrt(5/8 + sqrt(5)/8)/2 - sqrt(2)*(1/4 - sqrt(5)/4)/2) + (sqrt(5/8 + sqrt(5)/8)/2 - sqrt(3)*(1/4 - sqrt(5)/4)/2)*(sqrt(2)*sqrt(5/8 + sqrt(5)/8)/2 + sqrt(2)*(1/4 - sqrt(5)/4)/2) + (-sqrt(5/8 - sqrt(5)/8)/2 + sqrt(3)*(1/4 + sqrt(5)/4)/2)*(sqrt(2)*sqrt(5/8 - sqrt(5)/8)/2 - sqrt(2)*(1/4 + sqrt(5)/4)/2) + (sqrt(2)*sqrt(5/8 - sqrt(5)/8)/2 + sqrt(2)*(1/4 + sqrt(5)/4)/2)*(1/8 + sqrt(5)/8 + sqrt(3)*sqrt(5/8 - sqrt(5)/8)/2) + (sqrt(2)*sqrt(5/8 + sqrt(5)/8)/2 - sqrt(2)*(1/4 - sqrt(5)/4)/2)*(-1/8 + sqrt(5)/8 + sqrt(3)*sqrt(5/8 + sqrt(5)/8)/2) + (sqrt(2)*sqrt(5/8 + sqrt(5)/8)/2 - sqrt(2)*(1/4 - sqrt(5)/4)/2)*(1/8 - sqrt(5)/8 + sqrt(3)*sqrt(5/8 + sqrt(5)/8)/2) + (sqrt(2)*(1/4 + sqrt(5)/4)/2 - sqrt(2)*sqrt(5/8 - sqrt(5)/8)/2)*(-1/8 - sqrt(5)/8 + sqrt(3)*sqrt(5/8 - sqrt(5)/8)/2) + sqrt(2)*sqrt(5/8 - sqrt(5)/8)/2 + sqrt(2)*sqrt(5/8 + sqrt(5)/8)/2 + sqrt(2)*(1/4 + sqrt(5)/4)/2 + sqrt(3)*sqrt(5/8 - sqrt(5)/8)/2 + sqrt(3)*sqrt(5/8 + sqrt(5)/8)/2 + sqrt(3)*(1/4 + sqrt(5)/4)/2 - sqrt(2)*(1/4 - sqrt(5)/4)/2 + cos(pi/9) + cos(pi/18) + cos(pi/36) + cos(pi/45) + cos(pi/90) + cos(pi/180) + cos(2*pi/45) + cos(4*pi/45) + cos(5*pi/36) + cos(7*pi/36) + cos(7*pi/45) + cos(7*pi/90) + cos(7*pi/180) + cos(8*pi/45) + cos(11*pi/90) + cos(11*pi/180) + cos(13*pi/90) + cos(13*pi/180) + cos(17*pi/90) + cos(17*pi/180) + cos(19*pi/90) + cos(19*pi/180) + cos(23*pi/180) + cos(29*pi/180) + cos(31*pi/180) + cos(37*pi/180)

Respuesta numérica [src]

35.9450600353535502405945894843

35.9450600353535502405945894843

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 con funciones

Suma de la serie cos(n*pi/180)

Solución

Ejemplos de hallazgo de la suma de la serie