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Suma de la serie 3*((-1)^n-1)*cos(pi*n*x)/((2*pi^2*n^2))-(-1)^n*sin(pi*n*x)/(2*pi*n)



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Solución

Ha introducido [src]
  30                                                 
____                                                 
\   `                                                
 \    /  /    n    \                   n            \
  \   |3*\(-1)  - 1/*cos(pi*n*x)   (-1) *sin(pi*n*x)|
   )  |------------------------- - -----------------|
  /   |             2  2                 2*pi*n     |
 /    \         2*pi *n                             /
/___,                                                
n = 1                                                
$$\sum_{n=1}^{30} \left(- \frac{\left(-1\right)^{n} \sin{\left(x \pi n \right)}}{2 \pi n} + \frac{3 \left(\left(-1\right)^{n} - 1\right) \cos{\left(x \pi n \right)}}{2 \pi^{2} n^{2}}\right)$$
Sum(((3*((-1)^n - 1))*cos((pi*n)*x))/(((2*pi^2)*n^2)) - (-1)^n*sin((pi*n)*x)/((2*pi)*n), (n, 1, 30))
Respuesta [src]
               6*cos(5*pi*x)   6*cos(7*pi*x)   6*cos(11*pi*x)   6*cos(13*pi*x)   6*cos(17*pi*x)   6*cos(19*pi*x)   6*cos(23*pi*x)   6*cos(25*pi*x)   6*cos(29*pi*x)   2*cos(3*pi*x)   2*cos(9*pi*x)   2*cos(15*pi*x)   2*cos(21*pi*x)   2*cos(27*pi*x)   sin(2*pi*x)               sin(3*pi*x)   sin(5*pi*x)   sin(7*pi*x)   sin(9*pi*x)   sin(11*pi*x)   sin(13*pi*x)   sin(15*pi*x)   sin(17*pi*x)   sin(19*pi*x)   sin(21*pi*x)   sin(23*pi*x)   sin(25*pi*x)   sin(27*pi*x)   sin(29*pi*x)   sin(4*pi*x)   sin(6*pi*x)   sin(8*pi*x)   sin(10*pi*x)   sin(12*pi*x)   sin(14*pi*x)   sin(16*pi*x)   sin(18*pi*x)   sin(20*pi*x)   sin(22*pi*x)   sin(24*pi*x)   sin(26*pi*x)   sin(28*pi*x)   sin(30*pi*x)
-6*cos(pi*x) - ------------- - ------------- - -------------- - -------------- - -------------- - -------------- - -------------- - -------------- - -------------- - ------------- - ------------- - -------------- - -------------- - --------------   ----------- - sin(pi*x) - ----------- - ----------- - ----------- - ----------- - ------------ - ------------ - ------------ - ------------ - ------------ - ------------ - ------------ - ------------ - ------------ - ------------ + ----------- + ----------- + ----------- + ------------ + ------------ + ------------ + ------------ + ------------ + ------------ + ------------ + ------------ + ------------ + ------------ + ------------
                     25              49             121              169              289              361              529              625              841               3               27              75              147              243              2                         3             5             7             9             11             13             15             17             19             21             23             25             27             29             4             6             8             10             12             14             16             18             20             22             24             26             28             30     
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                                                                                                                            2                                                                                                                                                                                                                                                                                                                                                    2*pi                                                                                                                                                                                                                        
                                                                                                                        2*pi                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 
$$\frac{- 6 \cos{\left(\pi x \right)} - \frac{2 \cos{\left(3 \pi x \right)}}{3} - \frac{6 \cos{\left(5 \pi x \right)}}{25} - \frac{6 \cos{\left(7 \pi x \right)}}{49} - \frac{2 \cos{\left(9 \pi x \right)}}{27} - \frac{6 \cos{\left(11 \pi x \right)}}{121} - \frac{6 \cos{\left(13 \pi x \right)}}{169} - \frac{2 \cos{\left(15 \pi x \right)}}{75} - \frac{6 \cos{\left(17 \pi x \right)}}{289} - \frac{6 \cos{\left(19 \pi x \right)}}{361} - \frac{2 \cos{\left(21 \pi x \right)}}{147} - \frac{6 \cos{\left(23 \pi x \right)}}{529} - \frac{6 \cos{\left(25 \pi x \right)}}{625} - \frac{2 \cos{\left(27 \pi x \right)}}{243} - \frac{6 \cos{\left(29 \pi x \right)}}{841}}{2 \pi^{2}} - \frac{- \sin{\left(\pi x \right)} + \frac{\sin{\left(2 \pi x \right)}}{2} - \frac{\sin{\left(3 \pi x \right)}}{3} + \frac{\sin{\left(4 \pi x \right)}}{4} - \frac{\sin{\left(5 \pi x \right)}}{5} + \frac{\sin{\left(6 \pi x \right)}}{6} - \frac{\sin{\left(7 \pi x \right)}}{7} + \frac{\sin{\left(8 \pi x \right)}}{8} - \frac{\sin{\left(9 \pi x \right)}}{9} + \frac{\sin{\left(10 \pi x \right)}}{10} - \frac{\sin{\left(11 \pi x \right)}}{11} + \frac{\sin{\left(12 \pi x \right)}}{12} - \frac{\sin{\left(13 \pi x \right)}}{13} + \frac{\sin{\left(14 \pi x \right)}}{14} - \frac{\sin{\left(15 \pi x \right)}}{15} + \frac{\sin{\left(16 \pi x \right)}}{16} - \frac{\sin{\left(17 \pi x \right)}}{17} + \frac{\sin{\left(18 \pi x \right)}}{18} - \frac{\sin{\left(19 \pi x \right)}}{19} + \frac{\sin{\left(20 \pi x \right)}}{20} - \frac{\sin{\left(21 \pi x \right)}}{21} + \frac{\sin{\left(22 \pi x \right)}}{22} - \frac{\sin{\left(23 \pi x \right)}}{23} + \frac{\sin{\left(24 \pi x \right)}}{24} - \frac{\sin{\left(25 \pi x \right)}}{25} + \frac{\sin{\left(26 \pi x \right)}}{26} - \frac{\sin{\left(27 \pi x \right)}}{27} + \frac{\sin{\left(28 \pi x \right)}}{28} - \frac{\sin{\left(29 \pi x \right)}}{29} + \frac{\sin{\left(30 \pi x \right)}}{30}}{2 \pi}$$
(-6*cos(pi*x) - 6*cos(5*pi*x)/25 - 6*cos(7*pi*x)/49 - 6*cos(11*pi*x)/121 - 6*cos(13*pi*x)/169 - 6*cos(17*pi*x)/289 - 6*cos(19*pi*x)/361 - 6*cos(23*pi*x)/529 - 6*cos(25*pi*x)/625 - 6*cos(29*pi*x)/841 - 2*cos(3*pi*x)/3 - 2*cos(9*pi*x)/27 - 2*cos(15*pi*x)/75 - 2*cos(21*pi*x)/147 - 2*cos(27*pi*x)/243)/(2*pi^2) - (sin(2*pi*x)/2 - sin(pi*x) - sin(3*pi*x)/3 - sin(5*pi*x)/5 - sin(7*pi*x)/7 - sin(9*pi*x)/9 - sin(11*pi*x)/11 - sin(13*pi*x)/13 - sin(15*pi*x)/15 - sin(17*pi*x)/17 - sin(19*pi*x)/19 - sin(21*pi*x)/21 - sin(23*pi*x)/23 - sin(25*pi*x)/25 - sin(27*pi*x)/27 - sin(29*pi*x)/29 + sin(4*pi*x)/4 + sin(6*pi*x)/6 + sin(8*pi*x)/8 + sin(10*pi*x)/10 + sin(12*pi*x)/12 + sin(14*pi*x)/14 + sin(16*pi*x)/16 + sin(18*pi*x)/18 + sin(20*pi*x)/20 + sin(22*pi*x)/22 + sin(24*pi*x)/24 + sin(26*pi*x)/26 + sin(28*pi*x)/28 + sin(30*pi*x)/30)/(2*pi)

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