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Show that, $\lim\limits_{n\to \infty}n\sin(2\pi en!)=2\pi$

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marked as duplicate by Martin Sleziak, Marc van Leeuwen, Davide Giraudo, drhab, Sami Ben Romdhane 2 days ago

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Note that $e=\sum_{k=0}^\infty\frac1{k!}$, hence $en!=\sum_{k=0}^n\frac{n!}{k!}+\frac1{n+1}+\ldots$ is quite close to an integer.

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