Monday, November 6, 2017

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?

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