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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1/(n*(n+1)*(n+2))
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(2/9)^n
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1/n*(n+1)
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1/(n(n+2))
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Expresiones idénticas
- cos(n°)
- coseno de (n°)
- cosn°
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Expresiones semejantes
- cosn°
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Expresiones con funciones
- Coseno cos
- cos(pi*n)/(n-1)
- cosn^2+1/n^3+2
- cosn°
- cospin/3*(n+1)^4/3
- cos(pin)/(n-1)
Suma de la serie cos(n°)
Solución
Ha introducido
[src]
36 ___ \ ` \ /n*pi\ ) cos|----| / \360 / /__, n = 1
$$\sum_{n=1}^{36} \cos{\left(\frac{\pi n}{360} \right)}$$
Sum(cos((n*pi)/360), (n, 1, 36))
Velocidad de la convergencia de la serie
Respuesta
[src]
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___________ / 1 \/ 2 / 5 \/ 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 ___ |1 \/ 5 || | ___ / 5 \/ 5 || / ___________ ___________ ___________\ || / 5 \/ 5 ___ |1 \/ 5 || | ___ / 5 \/ 5 ___ |1 \/ 5 || | ___ |1 \/ 5 | ___ / 5 \/ 5 | | ___ / 5 \/ 5 || / ___________ ___________ ___________\ || / 5 \/ 5 ___ |1 \/ 5 || | ___ / 5 \/ 5 ___ |1 \/ 5 || | ___ / 5 \/ 5 ___ |1 \/ 5 || | ___ / 5 \/ 5 || / ___________ ___________ ___________ \ || / 5 \/ 5 ___ |1 \/ 5 || | ___ / 5 \/ 5 ___ |1 \/ 5 || | ___ |1 \/ 5 | ___ / 5 \/ 5 | | ___ / 5 \/ 5 || || / 5 \/ 5 ___ |1 \/ 5 || | ___ |1 \/ 5 | ___ / 5 \/ 5 | | ___ / 5 \/ 5 ___ |1 \/ 5 || | ___ / 5 \/ 5 || / ___________ ___________ ___________ \ | ___ |1 \/ 5 | ___ / 5 \/ 5 | | ___ / 5 \/ 5 | ___ / 5 \/ 5 ___ |1 \/ 5 | ___ / 1 \/ 2 ___ / 5 \/ 5 ___ |1 \/ 5 |
/ ___ / - - ----- / - - ----- ___ ___ ___ / ___ / ___ / ___ / ___\ / ___ / ___ / ___ / ___\ | / - - ----- \/ 3 *|- + -----|| |\/ 2 * / - - ----- \/ 2 *|- + -----|| | / ___ / ___ / ___ / ___\| || / - - ----- \/ 3 *|- + -----|| |\/ 2 * / - - ----- \/ 2 *|- + -----|| | \/ 2 * / - - ----- \/ 2 *|- + -----|| | ___ \/ 3 * / - - ----- || | / ___ / ___ / ___ / ___\| || / - - ----- \/ 3 *|- + -----|| |\/ 2 * / - - ----- \/ 2 *|- + -----|| |\/ 2 * / - - ----- \/ 2 *|- + -----|| | ___ \/ 3 * / - - ----- || | / ___ / ___\ / ___ / ___ | || / - - ----- \/ 3 *|- + -----|| |\/ 2 * / - - ----- \/ 2 *|- + -----|| |\/ 2 *|- + -----| \/ 2 * / - - ----- | | ___ \/ 3 * / - - ----- || | / ___ / ___\ / ___ / ___ | || / - + ----- \/ 3 *|- - -----|| |\/ 2 * / - + ----- \/ 2 *|- - -----|| |\/ 2 * / - + ----- \/ 2 *|- - -----|| | ___ \/ 3 * / - + ----- || | / ___ / ___ / ___ / ___\| || / - - ----- \/ 3 *|- + -----|| | \/ 2 * / - - ----- \/ 2 *|- + -----|| |\/ 2 *|- + -----| \/ 2 * / - - ----- | | ___ \/ 3 * / - - ----- || || / - + ----- \/ 3 *|- - -----|| |\/ 2 *|- - -----| \/ 2 * / - + ----- | | \/ 2 * / - + ----- \/ 2 *|- - -----|| | ___ \/ 3 * / - + ----- || | / ___ / ___ / ___ / ___\| |\/ 2 *|- + -----| \/ 2 * / - - ----- | | ___ \/ 3 * / - - ----- | \/ 2 * / - - ----- \/ 2 *|- + -----| \/ 3 * / - + ----- \/ 3 * / - + ----- \/ 3 *|- + -----|
1 / 5 \/ 5 \/ 2 4 \/ 8 8 \/ 2 \/ 6 \/ 5 / 1 \/ 2 / 5 \/ 5 / 1 \/ 2 | 1 \/ 5 | / 1 \/ 2 / 5 \/ 5 / 1 \/ 2 |1 \/ 5 | |\/ 8 8 \4 4 /| | \/ 8 8 \4 4 /| | / 1 \/ 2 / 5 \/ 5 / 1 \/ 2 |1 \/ 5 || || \/ 8 8 \4 4 /| | \/ 8 8 \4 4 /| | \/ 8 8 \4 4 /| | 1 \/ 5 \/ 8 8 || | / 1 \/ 2 / 5 \/ 5 / 1 \/ 2 |1 \/ 5 || || \/ 8 8 \4 4 /| | \/ 8 8 \4 4 /| | \/ 8 8 \4 4 /| |1 \/ 5 \/ 8 8 || | / 1 \/ 2 | 1 \/ 5 | / 1 \/ 2 / 5 \/ 5 | ||\/ 8 8 \4 4 /| | \/ 8 8 \4 4 /| | \4 4 / \/ 8 8 | | 1 \/ 5 \/ 8 8 || | / 1 \/ 2 |1 \/ 5 | / 1 \/ 2 / 5 \/ 5 | ||\/ 8 8 \4 4 /| | \/ 8 8 \4 4 /| | \/ 8 8 \4 4 /| |1 \/ 5 \/ 8 8 || | / 1 \/ 2 / 5 \/ 5 / 1 \/ 2 | 1 \/ 5 || ||\/ 8 8 \4 4 /| | \/ 8 8 \4 4 /| | \4 4 / \/ 8 8 | |1 \/ 5 \/ 8 8 || || \/ 8 8 \4 4 /| | \4 4 / \/ 8 8 | | \/ 8 8 \4 4 /| |1 \/ 5 \/ 8 8 || | / 1 \/ 2 / 5 \/ 5 / 1 \/ 2 | 1 \/ 5 || | \4 4 / \/ 8 8 | | 1 \/ 5 \/ 8 8 | \/ 8 8 \4 4 / \/ 2 4 \/ 8 8 \4 4 / /pi\ /pi\ /pi\ /pi\ /pi\ / pi\ / pi\ /2*pi\ /4*pi\ /5*pi\ /7*pi\ /7*pi\ /7*pi\ /7*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|-----|
8 \/ 8 8 2 2 4 4 8 \/ 2 4 \/ 8 8 \/ 2 4 \ 4 4 / \/ 2 4 \/ 8 8 \/ 2 4 \4 4 / \ 2 2 / \ 2 2 / \\/ 2 4 \/ 8 8 \/ 2 4 \4 4 // \\ 2 2 / \ 2 2 / \ 2 2 / \ 8 8 2 // \\/ 2 4 \/ 8 8 \/ 2 4 \4 4 // \\ 2 2 / \ 2 2 / \ 2 2 / \8 8 2 // \\/ 2 4 \ 4 4 / \/ 2 4 \/ 8 8 / \\ 2 2 / \ 2 2 / \ 2 2 / \ 8 8 2 // \\/ 2 4 \4 4 / \/ 2 4 \/ 8 8 / \\ 2 2 / \ 2 2 / \ 2 2 / \8 8 2 // \\/ 2 4 \/ 8 8 \/ 2 4 \ 4 4 // \\ 2 2 / \ 2 2 / \ 2 2 / \8 8 2 // \\ 2 2 / \ 2 2 / \ 2 2 / \8 8 2 // \ \/ 2 4 \/ 8 8 \/ 2 4 \ 4 4 // \ 2 2 / \ 8 8 2 / 2 2 2 2 2 \18/ \36/ \45/ \72/ \90/ \180/ \360/ \ 45 / \ 45 / \ 72 / \ 72 / \ 90 / \180 / \360 / \ 180 / \ 360 / \ 180 / \ 360 / \ 180 / \ 360 / \ 360 / \ 360 / \ 360 / \ 360 /
$$- \frac{1}{8} + \left(\left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right) \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} + \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right) \left(\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{5}}{8} - \frac{1}{8} + \frac{\sqrt{3} \sqrt{\frac{5}{8} - \frac{\sqrt{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{3} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\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) + \left(- \frac{1}{4} + \frac{\sqrt{5}}{4}\right) \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} + \left(- \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} - \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)\right) \left(\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{5}}{8} + \frac{1}{8} + \frac{\sqrt{3} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right) + \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{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} + \frac{\sqrt{3} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)}{2}\right)\right) + \frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \frac{\sqrt{5}}{8} + \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{\sqrt{2}}{4} + \left(- \left(- \frac{1}{4} + \frac{\sqrt{5}}{4}\right) \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} + \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right) \left(\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) + \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{3} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) + \frac{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \left(- \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right) \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} + \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right) \left(\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{1}{8} + \frac{\sqrt{5}}{8} + \frac{\sqrt{3} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) + \frac{\sqrt{2} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2} + \frac{\sqrt{6}}{4} + \frac{\sqrt{3} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{2} + \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right) \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} + \left(\left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right) \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} + \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right) \left(\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) + \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)\right) + \frac{\sqrt{3} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{3} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} + \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} + \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} + \cos{\left(\frac{7 \pi}{72} \right)} + \cos{\left(\frac{17 \pi}{180} \right)} + \cos{\left(\frac{4 \pi}{45} \right)} + \cos{\left(\frac{31 \pi}{360} \right)} + \cos{\left(\frac{29 \pi}{360} \right)} + \cos{\left(\frac{7 \pi}{90} \right)} + \cos{\left(\frac{13 \pi}{180} \right)} + \cos{\left(\frac{5 \pi}{72} \right)} + \cos{\left(\frac{23 \pi}{360} \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{19 \pi}{360} \right)} + \cos{\left(\frac{17 \pi}{360} \right)} + \cos{\left(\frac{2 \pi}{45} \right)} + \cos{\left(\frac{7 \pi}{180} \right)} + \cos{\left(\frac{13 \pi}{360} \right)} + \cos{\left(\frac{11 \pi}{360} \right)} + \left(\left(- \frac{1}{4} + \frac{\sqrt{5}}{4}\right) \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} + \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right) \left(\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) + \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)\right) + \cos{\left(\frac{\pi}{36} \right)} + \cos{\left(\frac{\pi}{45} \right)} + \cos{\left(\frac{7 \pi}{360} \right)} + \cos{\left(\frac{\pi}{72} \right)} + \cos{\left(\frac{\pi}{90} \right)} + \cos{\left(\frac{\pi}{180} \right)} + \cos{\left(\frac{\pi}{360} \right)}$$
-1/8 + sqrt(5/8 + sqrt(5)/8) + sqrt(1/2 - sqrt(2)/4)/2 + sqrt(5/8 - sqrt(5)/8)/2 + sqrt(2)/4 + sqrt(6)/4 + sqrt(5)/8 + sqrt(1/2 - sqrt(2)/4)*sqrt(5/8 - sqrt(5)/8) + sqrt(1/2 - sqrt(2)/4)*(-1/4 + sqrt(5)/4) + sqrt(1/2 + sqrt(2)/4)*sqrt(5/8 + sqrt(5)/8) + sqrt(1/2 + sqrt(2)/4)*(1/4 + sqrt(5)/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(1/2 - sqrt(2)/4)*sqrt(5/8 + sqrt(5)/8) + sqrt(1/2 + sqrt(2)/4)*(1/4 - sqrt(5)/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(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(1/2 - sqrt(2)/4)*sqrt(5/8 + sqrt(5)/8) - sqrt(1/2 + sqrt(2)/4)*(1/4 - sqrt(5)/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(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(1/2 - sqrt(2)/4)*(-1/4 + sqrt(5)/4) + sqrt(1/2 + sqrt(2)/4)*sqrt(5/8 + sqrt(5)/8))*((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)*(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(1/2 - sqrt(2)/4)*(1/4 + sqrt(5)/4) + sqrt(1/2 + sqrt(2)/4)*sqrt(5/8 - sqrt(5)/8))*((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(1/2 + sqrt(2)/4)*sqrt(5/8 + sqrt(5)/8) - sqrt(1/2 - sqrt(2)/4)*(-1/4 + sqrt(5)/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(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(5/8 + sqrt(5)/8)/2 + sqrt(3)*(1/4 - sqrt(5)/4)/2)*(sqrt(2)*(1/4 - sqrt(5)/4)/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)*(1/8 - sqrt(5)/8 + sqrt(3)*sqrt(5/8 + sqrt(5)/8)/2))*(-sqrt(1/2 - sqrt(2)/4)*sqrt(5/8 - sqrt(5)/8) - sqrt(1/2 + sqrt(2)/4)*(-1/4 - sqrt(5)/4)) + (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)*(1/4 + sqrt(5)/4)/2 + sqrt(3)*sqrt(1/2 + sqrt(2)/4)/2 + sqrt(3)*sqrt(5/8 + sqrt(5)/8)/2 + sqrt(3)*(1/4 + sqrt(5)/4)/2 + cos(pi/18) + cos(pi/36) + cos(pi/45) + cos(pi/72) + cos(pi/90) + cos(pi/180) + cos(pi/360) + cos(2*pi/45) + cos(4*pi/45) + cos(5*pi/72) + cos(7*pi/72) + cos(7*pi/90) + cos(7*pi/180) + cos(7*pi/360) + cos(11*pi/180) + cos(11*pi/360) + cos(13*pi/180) + cos(13*pi/360) + cos(17*pi/180) + cos(17*pi/360) + cos(19*pi/360) + cos(23*pi/360) + cos(29*pi/360) + cos(31*pi/360)
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