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Suma de la serie ((x+5)^(2n-1))/((4^n)*(2n-1))



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Solución

Ha introducido [src]
  oo                
____                
\   `               
 \           2*n - 1
  \   (x + 5)       
   )  --------------
  /     n           
 /     4 *(2*n - 1) 
/___,               
n = 1               
$$\sum_{n=1}^{\infty} \frac{\left(x + 5\right)^{2 n - 1}}{4^{n} \left(2 n - 1\right)}$$
Sum((x + 5)^(2*n - 1)/((4^n*(2*n - 1))), (n, 1, oo))
Respuesta [src]
/              /   __________\                         
|              |  /        2 |                         
|       2      |\/  (5 + x)  |                         
|(5 + x) *atanh|-------------|                         
|              \      2      /                         
|-----------------------------  for And(x > -7, x < -3)
|            __________                                
|           /        2                                 
|       2*\/  (5 + x)                                  
<                                                      
|      oo                                              
|    ____                                              
|    \   `                                             
|     \     -n        2*n                              
|      \   4  *(5 + x)                                 
|      /   --------------              otherwise       
|     /       -1 + 2*n                                 
|    /___,                                             
\    n = 1                                             
-------------------------------------------------------
                         5 + x                         
$$\frac{\begin{cases} \frac{\left(x + 5\right)^{2} \operatorname{atanh}{\left(\frac{\sqrt{\left(x + 5\right)^{2}}}{2} \right)}}{2 \sqrt{\left(x + 5\right)^{2}}} & \text{for}\: x > -7 \wedge x < -3 \\\sum_{n=1}^{\infty} \frac{4^{- n} \left(x + 5\right)^{2 n}}{2 n - 1} & \text{otherwise} \end{cases}}{x + 5}$$
Piecewise(((5 + x)^2*atanh(sqrt((5 + x)^2)/2)/(2*sqrt((5 + x)^2)), (x > -7)∧(x < -3)), (Sum(4^(-n)*(5 + x)^(2*n)/(-1 + 2*n), (n, 1, oo)), True))/(5 + x)

    Ejemplos de hallazgo de la suma de la serie