Question

Write the middle term in the expansion of ${\left(x+\frac{1}{x}\right)}^{10}$.

Answer 1

$$\begin{gathered} \mathrm{Here},n,\mathrm{i}.\mathrm{e}.,10,\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{number}. \\ \therefore \mathrm{Middle}\mathrm{term}=\left(\frac{10}{2}+1\right)\mathrm{th}\mathrm{term}=6\mathrm{th}\mathrm{term} \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ {T}_6=T_{5+1} \\ ={}^{10}C_5{\left(x\right)}^{10-5}\times {\left(\frac{1}{x}\right)}^5 \\ ={}^{10}C_5 \end{gathered}$$