# Stirling's formula?

Hi

I am looking to show that $\binom{|\mathbbm{F}| + n -1}{n} = \frac{1}{n!} |\mathbbm{F}|^n + O(|\mathbbm{F}|^{n-1})$

please could someone show me how??

How about writing the problem: for each $n$,
$$\binom{u+n-1}{n} = \frac{u^n}{n!} + O(u^{n-1}) \quad \text{as } u \to +\infty$$
If that is what you mean, first try to prove it for $n=1, n=2, n=3$ and see