If $$S=$$∑$$r=0m$$ $$n+rCk$$, then

Correct option is 2S+nCk+1=n+m+1Ck+1

Questions

If $S = \sum_{r = 0}^{m}^{n + r} C_{k}$ , then

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S+nCk+1=n+mCk+1

S+nCk+1=n+m+1Ck+1

S+nCk=n+mCk

None of these

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detailed solution

Correct option is B

S=∑r=0m n+rCk=nCk+n+1Ck+n+2Ck+…+n+mCk=nCk+1+nCk+n+1Ck+n+2Ck+…+n+mCk−nCk+1=n+1Ck+1+n+1Ck+n+2Ck+…+n+mCk−nCk+1∴ S=n+m+1Ck+1−nCk+1

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If S=∑r=0m n+rCk, then

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If $S = \sum_{r = 0}^{m}^{n + r} C_{k}$ , then