How to prove that $\lim\limits_{n\to\infty}\left(1+\frac{1}{p_n}\right)^{p_n}=e$?
Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$