Solution
= Solution
Let $a_n=n!/n^n$. Its consecutive coefficient ratio is
$$
\frac{a_{n+1}}{a_n}=\left(\frac n{n+1}\right)^n\longrightarrow e^{-1}.
$$
The <ratio test> for the full terms therefore has limit $|z|/e$: the series has <absolute convergence> when $|z|<e$ and its terms eventually grow in magnitude when $|z|>e$. Thus \b[the <radius of convergence> is] $\boxed{R=e}$. No boundary decision is needed to determine the <radius of convergence>.