I came up with $e = \sum_{n=0}^\infty \frac 1 {n!}$ (see here)
I am now trying to prove that this is equivalent to $\lim_{n\to \infty} {(1+\frac1 n)}^n$
In general, how would one go about such a task? Please do not prove what I stated above, I'd like to do that myself! Please tell me what conditions we have to satisfy to show that two expressions to infinity are equivalent?