Solution
= Solution
For the <sequence> in part (iii), part (ii) gives
$$
\left(\frac{n!}{n^n}\right)^{1/n}\longrightarrow e^{-1}.
$$
Taking reciprocals yields the <factorial-over-power series> <limit>
$$
\boxed{\lim_{n\to\infty}\frac{n}{(n!)^{1/n}}=e}.
$$