Stirling's formula?

  • Thread starter mathstime
  • Start date
  • #1
25
0

Main Question or Discussion Point

Hi

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

please could someone show me how??
 

Answers and Replies

  • #2
607
0
How about writing the problem: for each [itex]n[/itex],
[tex]
\binom{u+n-1}{n} = \frac{u^n}{n!} + O(u^{n-1})
\quad \text{as } u \to +\infty
[/tex]

If that is what you mean, first try to prove it for [itex]n=1, n=2, n=3[/itex] and see
if you understand those.
 
  • #3
25
0
got it! thanks!
 
Top