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

Question

Professor PC Thomas Classes · Answer

Sum of geometric series of binomials yields $\binom{16}{7} - \binom{6}{7}$. Coefficient of $x^6$ simplifies to $\binom{16}{6} - \binom{6}{5}$? Wait, $\binom{n+1}{r+1} - \binom{k}{r+1}$.