Prove $ \lim_\limits{n \to\infty}{(1 + \frac{1}{1!} + \frac{1}{2!} + \cdot\cdot\cdot + \frac{1}{n!})} = e $

Asked Mar 02 '15 at 06:32

Active Mar 02 '15 at 06:37

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Use that $ \lim_\limits{n \to \infty}{\left(1 + \frac{1}{n}\right)^n} = e $ to show that $ \lim_\limits{n \to \infty}{\left(1 + \frac{1}{1!} + \frac{1}{2!} + \cdot\cdot\cdot + \frac{1}{n!}\right)} = e $

I can't figure this one out. Can I get some help in solving this?

edited Mar 02 '15 at 06:37

asked Mar 02 '15 at 06:32

user3704351

The constant, Euler's number – user3704351 Mar 02 '15 at 06:35
use the taylor series for $e^x$, x=1, or use binomial thereom to expand. – MAM Mar 02 '15 at 06:35

Prove $ \lim_\limits{n \to\infty}{(1 + \frac{1}{1!} + \frac{1}{2!} + \cdot\cdot\cdot + \frac{1}{n!})} = e $

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