How to prove that $\lim_{n\to\infty}\sum_{k=1}^n\left(\frac{k}{n}\right)^n=\frac{e}{e-1}$?

Asked Mar 17 '15 at 11:34

Active Jun 09 '19 at 18:38

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How to prove that $$\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(\frac{k}{n}\right)^n=\frac{e}{e-1}$$

Thank in advances.

edited Jun 09 '19 at 18:38

StubbornAtom

asked Mar 17 '15 at 11:34

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Hi ! This look like a homework question : tell us what you've done and where you are stuck so users will give you usefull hints. – Tlön Uqbar Orbis Tertius Mar 17 '15 at 11:40

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