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Suma de la serie (x+2)^(2*n-1)/3^n



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Solución

Ha introducido [src]
  oo                
____                
\   `               
 \           2*n - 1
  \   (x + 2)       
   )  --------------
  /          n      
 /          3       
/___,               
n = 1               
$$\sum_{n=1}^{\infty} \frac{\left(x + 2\right)^{2 n - 1}}{3^{n}}$$
Sum((x + 2)^(2*n - 1)/3^n, (n, 1, oo))
Respuesta [src]
/             2            |       2|    
|      (2 + x)             |(2 + x) |    
|  ----------------    for ---------- < 1
|    /           2\            3         
|    |    (2 + x) |                      
|  3*|1 - --------|                      
|    \       3    /                      
<                                        
|  oo                                    
| ___                                    
| \  `                                   
|  \    -n        2*n                    
|  /   3  *(2 + x)         otherwise     
| /__,                                   
\n = 1                                   
-----------------------------------------
                  2 + x                  
$$\frac{\begin{cases} \frac{\left(x + 2\right)^{2}}{3 \left(1 - \frac{\left(x + 2\right)^{2}}{3}\right)} & \text{for}\: \frac{\left|{\left(x + 2\right)^{2}}\right|}{3} < 1 \\\sum_{n=1}^{\infty} 3^{- n} \left(x + 2\right)^{2 n} & \text{otherwise} \end{cases}}{x + 2}$$
Piecewise(((2 + x)^2/(3*(1 - (2 + x)^2/3)), Abs((2 + x)^2)/3 < 1), (Sum(3^(-n)*(2 + x)^(2*n), (n, 1, oo)), True))/(2 + x)

    Ejemplos de hallazgo de la suma de la serie