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Math Help - Calculate this sum

  1. #1
    Super Member dhiab's Avatar
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    Calculate this sum

    Calculate :
    S = \sum\limits_{p = 0}^n {C_p^n p^2 } \left( { - 3} \right)^p <br />
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Start with the binomial expansion (1+x)^n = \sum_{p=0}^n{n\choose p}x^p. Differentiate, multiply by x, differentiate again, multiply by x again, then put x=3.
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