# Calculate this sum

• August 28th 2009, 07:14 AM
dhiab
Calculate this sum
Calculate :
$S = \sum\limits_{p = 0}^n {C_p^n p^2 } \left( { - 3} \right)^p
$
• August 28th 2009, 11:50 PM
Opalg
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.