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Suma de la serie/ (pi*k*cos(kx)((-1)^k+1)+2sin(kx)((-1)^k-1))/k^3

Suma de la serie (pi*k*cos(kx)((-1)^k+1)+2sin(kx)((-1)^k-1))/k^3


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Solución

Ha introducido [src] 
  10                                                    
____                                                    
\   `                                                   
 \                  /    k    \              /    k    \
  \   pi*k*cos(k*x)*\(-1)  + 1/ + 2*sin(k*x)*\(-1)  - 1/
   )  --------------------------------------------------
  /                            3                        
 /                            k                         
/___,                                                   
k = 1
∑k=110πkcos⁡(kx)((−1)k+1)+((−1)k−1)2sin⁡(kx)k3\sum_{k=1}^{10} \frac{\pi k \cos{\left(k x \right)} \left(\left(-1\right)^{k} + 1\right) + \left(\left(-1\right)^{k} - 1\right) 2 \sin{\left(k x \right)}}{k^{3}} 
Sum((((pi*k)*cos(k*x))*((-1)^k + 1) + (2*sin(k*x))*((-1)^k - 1))/k^3, (k, 1, 10))
Respuesta [src] 
            4*sin(3*x)   4*sin(5*x)   4*sin(7*x)   4*sin(9*x)   pi*cos(2*x)   pi*cos(4*x)   pi*cos(6*x)   pi*cos(8*x)   pi*cos(10*x)
-4*sin(x) - ---------- - ---------- - ---------- - ---------- + ----------- + ----------- + ----------- + ----------- + ------------
                27          125          343          729            2             8             18            32            50
−4sin⁡(x)−4sin⁡(3x)27−4sin⁡(5x)125−4sin⁡(7x)343−4sin⁡(9x)729+πcos⁡(2x)2+πcos⁡(4x)8+πcos⁡(6x)18+πcos⁡(8x)32+πcos⁡(10x)50- 4 \sin{\left(x \right)} - \frac{4 \sin{\left(3 x \right)}}{27} - \frac{4 \sin{\left(5 x \right)}}{125} - \frac{4 \sin{\left(7 x \right)}}{343} - \frac{4 \sin{\left(9 x \right)}}{729} + \frac{\pi \cos{\left(2 x \right)}}{2} + \frac{\pi \cos{\left(4 x \right)}}{8} + \frac{\pi \cos{\left(6 x \right)}}{18} + \frac{\pi \cos{\left(8 x \right)}}{32} + \frac{\pi \cos{\left(10 x \right)}}{50} 
-4*sin(x) - 4*sin(3*x)/27 - 4*sin(5*x)/125 - 4*sin(7*x)/343 - 4*sin(9*x)/729 + pi*cos(2*x)/2 + pi*cos(4*x)/8 + pi*cos(6*x)/18 + pi*cos(8*x)/32 + pi*cos(10*x)/50

    Ejemplos de hallazgo de la suma de la serie

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