Q. The middle term in the expansion of $\left( x + \frac{1}{2x} \right)^{2n}$ is
A) $\frac{1 \bullet 3 \bullet 5\ldots(2n - 3)}{n!}$
B) $\frac{1 \bullet 3 \bullet 5\ldots(2n - 1)}{n!}$
C) $\frac{1 \bullet 3 \bullet 5\ldots(2n + 1)}{n!}$
D) None of these
Explanation
(b)
Given expansion is $\left( x + \frac{1}{2x} \right)^{2n}$
$\therefore Middle\ term = \ \ ^{2n}C_{n}\ {(x)}^{n}\left( \frac{1}{2x} \right)^{n}$
$= \frac{2n!}{n!n!2^{n}} = \frac{1 \bullet 3 \bullet 5\ldots(2n - 1)}{n!}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.