Sum of series i2^i-1

The solution

You have entered [src]

  oo           
 ___           
 \  `          
  \   /  i    \
  /   \i2  - 1/
 /__,          
i = 1

\sum_{i=1}^{\infty} \left(i_{2}^{i} - 1\right)

Sum(i2^i - 1, (i, 1, oo))

The answer [src]

      //   i2                  \
      || ------    for |i2| < 1|
      || 1 - i2                |
      ||                       |
      ||  oo                   |
-oo + |< ___                   |
      || \  `                  |
      ||  \     i              |
      ||  /   i2    otherwise  |
      || /__,                  |
      \\i = 1                  /

\begin{cases} \frac{i_{2}}{1 - i_{2}} & \text{for}\: \left|{i_{2}}\right| < 1 \\\sum_{i=1}^{\infty} i_{2}^{i} & \text{otherwise} \end{cases} - \infty

-oo + Piecewise((i2/(1 - i2), |i2| < 1), (Sum(i2^i, (i, 1, oo)), True))

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Sum of series i2^i-1

The solution

Examples of finding the sum of a series