Compound interest derivation of $e$ I'm reviewing stats and probability, including Poisson processes, and I came across:
$$e=\displaystyle \lim_{n\rightarrow \infty} \left(1+\frac{1}{n}\right)^n$$
I'd like to understand this more fully, but so far I'm struggling. I guess what I'm trying to understand is how you prove that it converges. Can anyone point me toward (or provide) a good explanation of this?

A great elementary proof is on Rudin's Principles of Mathematical Analysis page 64 Theorem 3.31.


PS: Sorry I don't know how to stretch it, maybe you can download the pic and enlarge.
