\(e=lim_{n \to \infty}e_{n}(1+\frac{1}{n})^n\\\)
\(=\lim_{n \to \infty}(\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\cdot\cdot+...\frac{1}{n!})\)
\(\lim_{n \to \infty}S_{n}=\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\cdot+\cdot+\frac{1}{n!}=e\)
原文：https://www.cnblogs.com/strongdady/p/13360943.html