Let Cr n denote the binomial coefficient of xr in the expansion of (1+x)n . ∑k=0102k+3k nCk=α·310+β.210,α,β∈R then α+β is equal to

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answer is 19.

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Detailed Solution

∑k=010Ck n2k+2+3k=22∑k=010Ck n2k+3∑k=010kCk n=41+210+3ddx1+x10x=1=4310+3029=4310+15210Here α=4,β=15∴α+β=19

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