Calculate:

$\displaystyle S = \sum\limits_{p = 0}^n {C_p^n p^2 } \left( { - 3} \right)^p

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- Aug 28th 2009, 07:14 AMdhiabCalculate this sum
**Calculate**:

$\displaystyle S = \sum\limits_{p = 0}^n {C_p^n p^2 } \left( { - 3} \right)^p

$ - Aug 28th 2009, 11:50 PMOpalg
Start with the binomial expansion $\displaystyle (1+x)^n = \sum_{p=0}^n{n\choose p}x^p$. Differentiate, multiply by x, differentiate again, multiply by x again, then put x=–3.