Question

The middle term in the expansion of ${(x-\frac{1}{x})}^{18}$ is

• A. ${}^{18}{C}_9$
• B. ${-}^{18}{C}_9$
• C. ${}^{18}{C}_{10}$
• D. ${-}^{18}{C}_{10}$

Answer 1

The correct option is B ${-}^{18}{C}_9$

The general term in the expansion ${(x-\frac{1}{x})}^{18}$ is given by
$T_{r+1}{=}^{18}{C}_r(x{)}^{18-r}{(-\frac{1}{x})}^r$
Here, $n=18$
$\therefore$ The middle term is $T_{9+1}$, where $r=9$
$\therefore T_{9+1}{=}^{18}{C}_9(-1{)}^9{x}^{18-2r}$
$={-}^{18}{C}_9{x}^{18-18}={-}^{18}{C}_9$