Question

Find the middle term (s) in the expansion of the following
${(x-\frac{1}{x})}^{10}$

Answer 1

Total number of terms $=10+1=11$

$\Rightarrow r+1=6$

$\Rightarrow r=6-1=5$

$\Rightarrow x=10$ $a=1$ $b=\frac{-1}{x}$

$({[x-\frac{1}{x}]}^{10}={\left[\frac{x^2-1}{x}\right]}^{10})$

$\Rightarrow n=10$ $a=1$ $b=\frac{-1}{x}$

$\Rightarrow {{}^{n}C}_r={{}^{n}C}_r{a}^{n-r}{b}^r$

Middle term $={{}^{10}C}_5{.1}^{10-5}{\left(\frac{-1}{x}\right)}^5$

$={{}^{10}C}_5.15\times \frac{1^5}{-x^5}$

$=-252.\frac{1}{x^5}$

Hence, solved.