Write the coefficient of the middle term in the expansion of

Here, $n$, i. e., $2 n$, is an even number.

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

Thus, we have :

$T_{n+1}={ }^{2 n} C_{n}(1)^{2 n-n}(x)^{n}$

$={ }^{2 n} C_{n} x^{n}$

Hence, the coefficient of the middle term is ${ }^{2 n} C_{n}$