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What could this limit be?

Calculus Level 4

$\Large \lim_{n \to \infty} \left(\frac {n!}{n^n} \right)^\frac 1n = \ ?$

1/e

Limit does not exist

\pi

1

\frac{\pi}{2}

0

e

\frac{\pi}{4}

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by Rishav Koirala

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