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Suma de la serie (6cos(nx)((-1)^n-cos(pi*n/3))/(pi*n^2)+sin(nx)((-2(-1)^n)/n+(6sin(pi*n/3))/(pi*n^2)))



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Solución

Ha introducido [src]
  2                                                                        
_____                                                                      
\    `                                                                     
 \     /           /    n      /pi*n\\            /                /pi*n\\\
  \    |6*cos(n*x)*|(-1)  - cos|----||            |       n   6*sin|----|||
   \   |           \           \ 3  //            |-2*(-1)         \ 3  /||
   /   |------------------------------ + sin(n*x)*|-------- + -----------||
  /    |                2                         |   n              2   ||
 /     \            pi*n                          \              pi*n    //
/____,                                                                     
n = 1                                                                      
$$\sum_{n=1}^{2} \left(\left(\frac{\left(-1\right) 2 \left(-1\right)^{n}}{n} + \frac{6 \sin{\left(\frac{\pi n}{3} \right)}}{\pi n^{2}}\right) \sin{\left(n x \right)} + \frac{\left(\left(-1\right)^{n} - \cos{\left(\frac{\pi n}{3} \right)}\right) 6 \cos{\left(n x \right)}}{\pi n^{2}}\right)$$
Sum(((6*cos(n*x))*((-1)^n - cos((pi*n)/3)))/((pi*n^2)) + sin(n*x)*((-2*(-1)^n)/n + (6*sin((pi*n)/3))/((pi*n^2))), (n, 1, 2))
Respuesta [src]
                                                   /  3*cos(x)   3*cos(2*x)\
/         ___\            /        ___\          6*|- -------- + ----------|
|     3*\/ 3 |            |    3*\/ 3 |            \     2           8     /
|-1 + -------|*sin(2*x) + |2 + -------|*sin(x) + ---------------------------
\       4*pi /            \       pi  /                       pi            
$$\frac{6 \left(- \frac{3 \cos{\left(x \right)}}{2} + \frac{3 \cos{\left(2 x \right)}}{8}\right)}{\pi} + \left(\frac{3 \sqrt{3}}{\pi} + 2\right) \sin{\left(x \right)} + \left(-1 + \frac{3 \sqrt{3}}{4 \pi}\right) \sin{\left(2 x \right)}$$
(-1 + 3*sqrt(3)/(4*pi))*sin(2*x) + (2 + 3*sqrt(3)/pi)*sin(x) + 6*(-3*cos(x)/2 + 3*cos(2*x)/8)/pi

    Ejemplos de hallazgo de la suma de la serie