 Factorial-over-power series

ID: factorial-over-power-series

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

a_{n} = n! / n^{n}

\frac{a _{n + 1}}{a _{n}} = (\frac{n}{n + 1})^{n} \to e^{- 1} .

Thus

\sum n! / n^{n}

converges and

n / (n!)^{1/ n} \to e

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