Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|cite|improve this question
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 ... – 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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.