Question

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

Answer 1

`x < 1/2`

Explanation:

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`