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Stirling's formula?

  1. Mar 5, 2010 #1
    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??
     
  2. jcsd
  3. Mar 5, 2010 #2
    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.
     
  4. Mar 6, 2010 #3
    got it! thanks!
     
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