Radius of convergence of $\sum_{n=0}^{\infty}{\frac{n!}{n^n}}x^n$ and $x\in \mathbb{C}$

52 Views Asked by At

i computed $|x|<e$ by using $\lim\limits_{n\to\infty}\bigg |\frac{a_{n}}{a_{n+1}}\bigg |$. But shouldn't there be more solutions since $x\in \mathbb{C}$?