Sr Examen
Otras calculadoras
- Serie de Taylor paso a paso
- Serie de Fourier paso a paso
- Ecuaciones diferenciales paso a paso
- Producto de la serie
-
¿Cómo usar?
- Suma de la serie:
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n^2/2^n
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((-1)^(n+1))/n
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(1/3)^n
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(3/7)^n
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Expresiones idénticas
- cos(pi*n/ ciento ochenta)
- coseno de ( número pi multiplicar por n dividir por 180)
- coseno de ( número pi multiplicar por n dividir por ciento ochenta)
- cos(pin/180)
- cospin/180
- cos(pi*n dividir por 180)
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Expresiones semejantes
- cos((pi*n)/180)
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Expresiones con funciones
- Coseno cos
- cos*2*n*x/4*n^2-1
- cos((n*pi)/180)
- cos(x+y)
- cos(sqrt(n))/sqrt(n)
- cos(n)(pi*2)/n^4
- Número Pi pi
- pi
- pi^(((-n)/pi)^n)
- pi^n/pi^n
- pi^(2*n)*(-1^n)/factorial(2*n)
- pi*n/n^2
Suma de la serie cos(pi*n/180)
Solución
Ha introducido
[src]
36 ___ \ ` \ /pi*n\ ) cos|----| / \180 / /__, n = 1
$$\sum_{n=1}^{36} \cos{\left(\frac{\pi n}{180} \right)}$$
Sum(cos((pi*n)/180), (n, 1, 36))
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 | | ___ / 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 *|- + -----|| |\/ 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 /| |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\ /23*pi\ /29*pi\ /31*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|-----|
4 \/ 8 8 2 2 2 4 4 \ 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 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 / \ 180 / \ 180 / \ 180 / \ 180 /
$$\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{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} + \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(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/180) + cos(23*pi/180) + cos(29*pi/180) + cos(31*pi/180)
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