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Question Number 118777 by obaidullah last updated on 19/Oct/20

$$\underset{n\to \mathrm{\infty }}{\lim }{\left(\frac{n!}{n^n}\right)}^{\frac{1}{n}}=\underset{n\to \mathrm{\infty }}{\lim }{\left(\frac{\sqrt{2n\pi }{n}^n}{n^n\times e^n}\right)}^{\frac{1}{n}}$$$$\Rightarrow \underset{n\to \mathrm{\infty }}{\lim }\frac{1}{e}{\left(\sqrt{2n\pi }\right)}^{\frac{1}{n}}=\frac{1}{e}$$

Answered by mathmax by abdo last updated on 19/Oct/20

$$\mathrm{where}\mathrm{is}\mathrm{the}\mathrm{Question}?$$

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