How do i find the limit and the convergence area for sum(x/(1-x))^n for x in RR // {1} ?

Mar 15, 2018

$x < \frac{1}{2}$

Explanation:

Calling $y = \frac{x}{1 - x}$

we have that for $\left\mid y \right\mid < 1$

${\sum}_{k = 0}^{\infty} {y}^{k}$ converges to $\frac{1}{1 - y}$ or

$\left\mid \frac{x}{1 - x} \right\mid < 1 \Rightarrow \left\mid x \right\mid < \left\mid 1 - x \right\mid \Rightarrow x < \frac{1}{2}$