I'm asked to show this on a problem I'm working on.
$e^{\frac{-n^2}{2K}}$ is an approximation of $\frac{k!}{k^n(k-n)!}$ when $n$ is large.
However in this class we've never gone over $e$, so the only forumula I know is $e^x = \lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n$. I don't see how to use that. Is there another forumula or method I'm not see or aware of? Any help is greatly appreciated. Thanks