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Summation with combinations

  1. Oct 8, 2013 #1
    1. The problem statement, all variables and given/known data

    I'm trying to derive the PGF for the Binomial.

    3. The attempt at a solution

    I have it whittled down to [itex]\sum^{n}_{x=0}(nCx)(\frac{sp}{1-p})^x[/itex]

    I just don't know how to simplify this further. Any help is most appreciated.
  2. jcsd
  3. Oct 9, 2013 #2


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    I think you lost some ##(1 - p)##s there, are you sure you didn't mean ##\sum_{x = 0}^n \binom{n}{x} (sp)^x (1 - p)^{n - x}##?

    The result should follow from the binomial theorem,
    $$ (x + y )^n = \sum_{k = 0}^n \binom{n}{k} x^{n-k} y^k. $$
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