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.2n−1
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B
0
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C
2n−1.(2−n)
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D
none of these
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Solution
The correct option is B0 ThegeneraltermisgivenbyTr=(−1)r.(r+1)CrHencetheseriesisgivenby∑n0(−1)r.(r+1)Cr=∑n0(−1)r.rCr+∑n0(−1)rCrSinceC0−C1+C2−C3+....=0andrCr=nCn−1r−1Henceusingtheabovetworelationwecanimplythatthesumofallthetermsintheserieswillbecome0