Tuesday, 18 June 2013

binomial coefficients - Proof by induction of sumnk=2(k1)(k)binomnk=n(n1)2n2

I've been struggling with this sum for an while, pluging n+1 instead of n, knowing that \binom{n+1}{k} = \binom{n}{k-1} + \binom{n}{k} and after some manipulation i've found this sum.
2\sum_{k=1}^{n} k^2\binom{n}{k}

I coudn't see any way I could get out of here and I don't know how to start this proof without the property of the sum of binomial coefficients.



Thanks in advance.

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