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How to solve the following limit? $$\lim_{N\rightarrow+\infty}\frac{1}{N}\sum_{k=1}^{N-1}\left(\frac{k}{N}\right)^N$$

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    Are you familiar with Riemann sums associated to Riemann integrals?2012-08-26
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    There is a celebre limit that states that if $\lim_{n\to\infty} a_{n} = a \geq 0$ and $\lim_{n\to\infty} b_{n} = b \geq 0$ then we have that $ \lim_{n\to\infty} \frac{a_{1} b_{n} + a_{2} b_{n-1}+ \cdots +a_{n} b_{1}}{n} =ab.$ I think this could be an alternative.2012-08-26

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