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

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Answer 1 · 2018-03-15T21:40:54

$x < 1/2$

Calling $y = x/(1-x)$

we have that for $abs y < 1$

$sum_(k=0)^oo y^k$ converges to $1/(1-y)$ or

$abs(x/(1-x)) < 1 rArr abs x < abs(1-x) rArr x < 1/2$

How do i find the limit and the convergence area for sum(x/(1-x))^n∑(x1−x)nsum(x/(1-x))^n for x in RR // {1}x in RR // {1} ?