Question

Find the middle term of ${(\frac{a}{x}+\frac{x}{a})}^{10}$.

Answer 1

The expansion of $(1+x{)}^n$ has n+1 terms,

$\therefore 6^{th}$ term will be the middle term in the expansion

We know that the $r^{th}$ term in expansion of $(a+x{)}^n$ is given by ${}^n{C}_{r-1}{a}^{n+1-r}{x}^{r-1}$

$\therefore$ $6^{th}$ term in the expansion of ${(\frac{a}{x}+\frac{x}{a})}^{10}$ is the middle term which equals ${}^{10}{C}_5{\left(\frac{a}{x}\right)}^5{\left(\frac{x}{a}\right)}^5=252$