23rd Putnam 1962

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Problem A5

Find nC1 12 + nC2 22 + nC3 32 + ... + nCn n2 (where nCr is the binomial coefficient).

 

Solution

Answer: n(n+1)2n-2.

Differentiate (1 + x)n, multiply by x and differentiate again. Set x = 1.

 


 

23rd Putnam 1962

© John Scholes
jscholes@kalva.demon.co.uk
5 Feb 2002