# Write the middle term in the expansion of

Question:

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

Solution:

Here, $n$, i. e., 10 , is an even number.

$\therefore$ Middle term $=\left(\frac{10}{2}+1\right)$ th term $=6$ th term

Thus, we have:

$T_{6}=T_{5+1}$

$={ }^{10} C_{5}(x)^{10-5} \times\left(\frac{1}{x}\right)^{5}$

$={ }^{10} C_{5}$