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  4. The middle term in the expansion of (1 + x)2n is

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Q. The middle term in the expansion of $(1 + x)^{2n}$ is

Binomial Theorem

Solution:

Middle term in $(1 + x)^{2n} = T_{n+1}$
$= \,{}^{2n}c_{n}x^{n} = \frac{2n\,!}{n\,!\,n\,!}$
$= \frac{\left[1.3.5...... \left(2n - 1\right)\right] \left[2.4.6...2n\right]}{n\,!\,n\,!}$
$= \frac{\left[1.3.5.......\left(2n - 1\right)\right]2^{n}}{n\,!}x^{n}$