Mathematics - Binomial Theorem Question with Solution | TestHub

Given, $17^{\text{th }}$ and $18^{\text{th }}$ terms in the expansion $(2+a{)}^{50}$ are equal $\therefore T_{17}=T_{18}$ $\Rightarrow {}^{50}{C}_{16}(2{)}^{34}(a{)}^{16}={}^{50}{C}_{17}(2{)}^{33}(a{)}^{17}$ $\Rightarrow a=\frac{{}^{50}{C}_{16}}{{}^{50}{C}_{17}}\times 2=1$ $\therefore$ Now, coefficient of $x^{35}$ in the expansion $(1+x{)}^{-2}=-36$ $\because$ Coefficient of $x^r$ is $(r+1)$ in $(1-x{)}^{-2}$.