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Factorials approximation problem

  1. Feb 25, 2008 #1
    1. The problem statement, all variables and given/known data
    How is,

    [(N+Q)!Q!]/[(Q+1)!(N+Q-1)!] equal to (N+Q)/(Q+1) when N,Q>>1 ??

    It looks like the Q!/(N+Q-1)! cancels but i don't see how, im going from my lecturers notes here.
    2. Relevant equations

    3. The attempt at a solution
    Last edited: Feb 25, 2008
  2. jcsd
  3. Feb 25, 2008 #2
    Break it up - look at the fraction as

    [tex]\frac{Q!}{(Q+1)!} \cdot \frac{(N+Q)!}{(N+Q-1)!}[/tex]

    For the first fraction, ask yourself "what number you would multiply [itex]Q![/itex] by to get [itex](Q+1)![/itex]"?

    Do a similar analysis for the second fraction.
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