MathDB
Today's calculation of Integral 199

Source:

April 23, 2007
calculusintegrationcalculus computations

Problem Statement

Let m, nm,\ n be non negative integers. Calculate ∑k=0n(−1)kn+m+1k+m+1 nCk.\sum_{k=0}^{n}(-1)^{k}\frac{n+m+1}{k+m+1}\ nC_{k}. where iCj_{i}C_{j} is a binomial coefficient which means i⋅(i−1)⋯(i−j+1)j⋅(j−1)⋯2⋅1\frac{i\cdot (i-1)\cdots(i-j+1)}{j\cdot (j-1)\cdots 2\cdot 1}.
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