The coefficient of $x^8$ in $\left\{(1+x)^6+(1+x)^7+\ldots+(1+x)^{15}\right\}$ is

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Professor PC Thomas Classes · Answer

Sum of geometric progression of binomials $\Rightarrow \frac{(1+x)^{16} - (1+x)^6}{(1+x)-1}$. Coeff of $x^8$ is ${}^{16}C_9 = {}^{16}C_7$.