# Math Help - Radii of convergence

1. This is question.I need to sovle exacly the same problem like #5 but teacher told us that in the proof we should use the fact that (1+(1/n))^n goes to e.

2. Originally Posted by drpawel
This is question.I need to sovle exacly the same problem like #5 but teacher told us that in the proof we should use the fact that (1+(1/n))^n goes to e.
\begin{aligned}\lim_{n\to\infty}\left|\frac{(n+1)^ {n+1}x^{n+1}}{(n+1)!}\cdot\frac{n!}{n^nx^n}\right| &=|x|\lim_{n\to\infty}\left|\frac{(n+1)^{n}}{n^n}\ right|\\