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Consider: $$\lim_{n \rightarrow\infty} \sum_{k=0}^n {n\choose k} \frac{1}{n^k}$$ One might consider using the binomial expansion to obtain: $$\lim_{n \rightarrow\infty}\left(1+\frac{1}{n}\right)^n $$ Which equals $e$. My question is: How can I write the first limit as an integral over some interval of some function? Is it an elementary function? Thanks.

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  • $\begingroup$ Are you looking to write the sum as a Riemann sum? $\endgroup$ – Mark Viola May 13 '17 at 3:19

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