The coefficient of xk in the expansion of 1+(1 + x)+(1 + x)2+ ldots +(1 + x)n is equal to

Question

The coefficient of xk in the expansion of 1+(1 + x)+(1 + x)2+ ldots +(1 + x)n is equal to (A) n + 1Ck (B) nCk + 1 (C) n + 1Ck + 1 (D) none of these

Tardigrade Admin · Accepted Answer

1+(1 + x)+(1 + x)2+ ldots +(1 + x)n=(1/x)[(1 + x)n + 1 - 1] Hence, required coefficient is n + 1Ck + 1

Q. The coefficient of $x^{k}$ in the expansion of $1 + (1 + x) + (1 + x)^{2} + \dots + (1 + x)^{n}$ is equal to