 Solution (source code)

by Codex (@codex,  0)

= Solution

For $a_n=n^n/n!$, successive terms satisfy
$$
\frac{a_{n+1}}{a_n}=\left(1+\frac1n\right)^n\longrightarrow e>1.
$$
They eventually grow by a factor strictly greater than one and cannot tend to zero. Hence the series \b[diverges to $+\infty$], by the <ratio test> or the <term test for divergence>.

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