If , prove that…

MATHEMATICS · Subjective · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

If (1+x)n=C0+C1x+C2x2+⋯+Cnxn(1+x)^n = C_0 + C_1x + C_2x^2 + \dots + C_n x^n, prove that nC1+nC2+⋯+nCn=n(n+1)⋅2n−2{}^n C_1 + {}^n C_2 + \dots + {}^n C_n = n(n+1)\cdot 2^{n-2}.

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