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

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


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Solución

Ha introducido [src] 
  36           
 ___           
 \  `          
  \      /pi*n\
   )  cos|----|
  /      \180 /
 /__,          
n = 1
∑n=136cos⁡(πn180)\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
1.07.01.52.02.53.03.54.04.55.05.56.06.5010
Respuesta [src] 
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        /       ___      ___     ___     /   - - -----      ___     ___   |  /   - - -----    \/ 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 /
(−2(14+54)2+258−582)(−58−582+3(14+54)2)+(−258−582+2(14+54)2)(−58−18+358−582)−2(14−54)2+14+58−582+(2(14−54)2+258+582)(−3(14−54)2+58+582)+24+258−582+358−582+2(14+54)2+(−2(14−54)2+258+582)(−58+18+358+582)+64+258+582+3(14+54)2+cos⁡(7π36)+358+582+cos⁡(17π90)+cos⁡(8π45)+cos⁡(31π180)+32+cos⁡(29π180)+cos⁡(7π45)+cos⁡(13π90)+(258−582+2(14+54)2)(18+58+358−582)+cos⁡(5π36)+cos⁡(23π180)+cos⁡(11π90)+cos⁡(π9)+cos⁡(19π180)+58+58+cos⁡(17π180)+cos⁡(4π45)+cos⁡(7π90)+cos⁡(13π180)+cos⁡(11π180)+(258−582+2(14+54)2)(58−582+3(14+54)2)+cos⁡(π18)+cos⁡(2π45)+cos⁡(7π180)+cos⁡(π36)+cos⁡(π45)+cos⁡(π90)+cos⁡(π180)+52\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)
Respuesta numérica [src] 
33.5812678102425645576366731487
33.5812678102425645576366731487
Gráfico
Suma de la serie cos(pi*n/180)

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