Proof for closed form approximation of e

Asked Jun 15 '13 at 10:43

Active Jun 15 '13 at 11:20

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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?

asked Jun 15 '13 at 10:43

T. Webster

3,052

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
2

Here and here and ... – Start wearing purple 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

Proof for closed form approximation of e

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