For which p the series converge? $$\sum_{n=0}^{\infty}\left(\frac{1}{n!}\right)^{p}$$
Please verify answer below

Comparison test
$$\lim_{n\rightarrow\infty}\left(\frac{n!}{(n+1)!}\right)^{p}=\frac{1}{(n+1)^{p}}=\begin{cases}
1 & \Leftrightarrow p=0\\
0 & \Leftrightarrow p\neq0
\end{cases}$$
The series have the same convergence as $\frac{1}{n}$, so for:


*

*$p>1$ converge

*for $p<1$ don't converge

