power series - Proof for closed form approximation of e

I am familiar with the derivation of $e$ from a power series, $e = \sum_{k=0}^{\infty} \frac{1}{k!}$ but have not found the proof for

the following representation in any textbook

$e = \lim_{x\ \to \infty} (1+ \frac{1}{x})^{x}$

What is the proof or where might I find it?