Proof that $\lim_{n \to \infty} ( 1+\frac{1}{a_n}) ^ {a_n} = e$ if $\lim_{n \to \infty}a_n = \infty$.
Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$