Stirling's formula?

[mathstime]

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??

[g_edgar]

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
if you understand those.

[mathstime]

got it! thanks!