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



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Solución

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

    Ejemplos de hallazgo de la suma de la serie