Write the coefficient of the middle term in the expansion of

Question:

Write the coefficient of the middle term in the expansion of $(1+x)^{2 n}$.

Solution:

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 ${ }^{2 n} C_{n}$

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