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



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Solución

Ha introducido [src]
  oo                 
____                 
\   `                
 \          n + 1    
  \        x         
  /   ---------------
 /    (n + 1)*(n + 2)
/___,                
n = 1                
$$\sum_{n=1}^{\infty} \frac{x^{n + 1}}{\left(n + 1\right) \left(n + 2\right)}$$
Sum(x^(n + 1)/(((n + 1)*(n + 2))), (n, 1, oo))
Respuesta [src]
  //  /6 - 3*x   (6 - 6*x)*log(1 - x)\              \
  ||x*|------- + --------------------|              |
  ||  |    2               3         |              |
  ||  \   x               x          /              |
  ||----------------------------------  for |x| <= 1|
  ||                6                               |
  ||                                                |
  ||          oo                                    |
x*|<        ____                                    |
  ||        \   `                                   |
  ||         \          n                           |
  ||          \        x                            |
  ||           )  ------------           otherwise  |
  ||          /        2                            |
  ||         /    2 + n  + 3*n                      |
  ||        /___,                                   |
  \\        n = 1                                   /
$$x \left(\begin{cases} \frac{x \left(\frac{6 - 3 x}{x^{2}} + \frac{\left(6 - 6 x\right) \log{\left(1 - x \right)}}{x^{3}}\right)}{6} & \text{for}\: \left|{x}\right| \leq 1 \\\sum_{n=1}^{\infty} \frac{x^{n}}{n^{2} + 3 n + 2} & \text{otherwise} \end{cases}\right)$$
x*Piecewise((x*((6 - 3*x)/x^2 + (6 - 6*x)*log(1 - x)/x^3)/6, |x| <= 1), (Sum(x^n/(2 + n^2 + 3*n), (n, 1, oo)), True))

    Ejemplos de hallazgo de la suma de la serie