A funny limit of a sequence – math.stackexchange.com

A funny limit of a sequence – math.stackexchange.com

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Evaluate $$\lim_{n \rightarrow +\infty} \frac{\sin\frac{1}{n}+\sin \frac{2}{n}+\dots+\sin\frac{n}{n}}{e^{-\frac{1}{n}}+e^{-\frac{2}{n}}+\dots+e^{-\frac{n}{n}}}.$$

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