How to prove that:

$$\lim_{n\to\infty} \frac{1^n+2^n+\cdots+n^n}{n^n} = \frac{e}{e-1}$$

Any help is appreciated.


marked as duplicate by Carl Schildkraut, Parcly Taxel, Community Sep 27 '17 at 5:12

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  • $\begingroup$ @SangchulLee Thank you for your link,I see. $\endgroup$ – JamesJ Sep 27 '17 at 5:10