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The coefficient of $x^{k}$ in the expansion of $E = 1 + (1 + x) + (1 + x)^{2} + \dots + (1 + x)^{n}$ is

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nCk

n+1Ck

n+1Ck+1

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detailed solution

Correct option is C

We have E=1+(1+x)+(1+x)2+…+(1+x)n =1−(1+x)n+11−(1+x)=1x(1+x)n+1−1Thus, coefficient of xk in E = Coefficient of xk+1 in (1+x)n+1−1 =n+1Ck+1

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The coefficient of xk in the expansion of E=1+(1+x)+(1+x)2+…+(1+x)n is

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The coefficient of $x^{k}$ in the expansion of $E = 1 + (1 + x) + (1 + x)^{2} + \dots + (1 + x)^{n}$ is