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Question

Mathematics Question on Binomial theorem

If C0,C1,C2,…,CnC_{0}, C_{1}, C_{2}, \ldots, C_{n} denote the coefficients in the expansion of (1+x)n(1+x)^{n}, then the value of C1+2C2+3C3+…+nCnC_{1}+2C_{2}+3C_{3}+\ldots+nC_{n} is

A

n⋅2n−1n\cdot2^{n-1}

B

(n+1)2n−1(n+1)2^{n-1}

C

(n+1)2n(n+1)2^{n}

D

(n+2)2n−1(n+2)2^{n-1}

Answer

n⋅2n−1n\cdot2^{n-1}

Explanation

Solution

Since,