# Power Series : Interval of Convergence

Find the interval $I$ and radius of convergence $R$ for the given power series. $$\sum_{n=1}^\infty \frac {5^n}{n}x^{n}$$

What I got was that I used the limit as it goes to infinity I ended up with $x = 1/5$ for the radius and the interval I got $[-1/5,1/5)$. But this answer turned out to be wrong.

• Your answer is OK for me ... We have $$-\ln (1-x) =\sum_{n=1}^{\infty}\frac{x^n}{n},\quad |x|<1,$$ and the case $x=-1$ is also OK. – Olivier Oloa Feb 12 '15 at 3:12
• Oh, Ok thanks :) – user214862 Feb 12 '15 at 3:14