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

  //     1 + x                       \
  ||     -----        for |1 + x| < 1|
  ||        2                        |
  ||       x                         |
  ||                                 |
  ||  oo                             |
2*|< ___                             |
  || \  `                            |
  ||  \            n                 |
  ||  /   n*(1 + x)      otherwise   |
  || /__,                            |
  ||n = 1                            |
  \\                                 /
--------------------------------------
                1 + x                 

$$\frac{2 \left(\begin{cases} \frac{x + 1}{x^{2}} & \text{for}\: \left|{x + 1}\right| < 1 \\\sum_{n=1}^{\infty} n \left(x + 1\right)^{n} & \text{otherwise} \end{cases}\right)}{x + 1}$$

2*Piecewise(((1 + x)/x^2, |1 + x| < 1), (Sum(n*(1 + x)^n, (n, 1, oo)), True))/(1 + x)