### Definition $e=\lim _{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^{n}$ #### Related representations $\frac{1}{e}=\lim_{k\rightarrow\infty}\left(1-\frac{1}{k}\right)^{k}$ $e=\sum_{n=0}^{\infty} \frac{1}{n !}=1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\cdots$ $\frac{1}{e}=\sum_{k=0}^{\infty} \frac{(-1)^{k}}{k !}=1-\frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\cdots$ included in [[Euler's Identity]] [[𝑒^x - Exponential Function]]