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.
2026-05-16 15:16:08.1778944568
Integral form of a limit
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