lim-n-n-1-n-n-

Question Number 182659 by mathlove last updated on 12/Dec/22

\lim_{n \to \infty} \frac{\sqrt[n]{n!}}{n} = ?

Answered by Frix last updated on 12/Dec/22

n! \sim \frac{n^{n} \sqrt{2 π n}}{e^{n}}

\lim_{n \to \infty} \frac{\sqrt[n]{n!}}{n} = \lim_{n \to \infty} \frac{{(2 π n)}^{\frac{1}{2 n}}}{e} = \frac{1}{e}

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