Compute the radius of convergence of the power series $\sum_{n=0}^{\infty} n!x^n$ I need help with how to compute the radius of convergence of the power series $\sum_{n=0}^{\infty} n!x^n$?
I was thinking of using the ratio test but am unsure of how to go about it. Any help would be greatly appreciated, thanks

The ratio test does apply !
Putting $a_n=n!$ we see that :
$$\left|\frac{a_{n+1}}{a_n}\right|=\frac{(n+1)!}{n!}=n+1\underset{n\to\infty}{\longrightarrow}+\infty$$
Hence : $R=0$
In other words, this power series converges solely for $x=0$.
