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Question

If C0,C1,C2,.....Cn are binomial coefficients of different terms in the expansion of (1+x)n then C0+2.C1+3.C2+4.C3+....+(1)n.(n+1)Cn equals

A
n.2n1
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B
0
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C
2n1.(2n)
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D
none of these
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Solution

The correct option is B 0
ThegeneraltermisgivenbyTr=(1)r.(r+1)CrHencetheseriesisgivenbyn0(1)r.(r+1)Cr=n0(1)r.rCr+n0(1)rCrSinceC0C1+C2C3+....=0andrCr=nCn1r1Henceusingtheabovetworelationwecanimplythatthesumofallthetermsintheserieswillbecome0

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