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?

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As I can recall in the textbook, the e is defined first by a limit (1+1/n)^n for n goes to infinity. –  eccstartup Jun 15 '13 at 10:48
Here and here and ... –  L.G. Jun 15 '13 at 10:48
@eccstartup, I think his question is essentially that if $e$ is defined by that series, how you show it is equivalent to the limit definition. –  Christopher A. Wong Jun 15 '13 at 10:49
@Christopher A. Wong, I think many textbooks on analysis have the proof of the equivalence. –  eccstartup Jun 15 '13 at 10:59