The middle term in the expansion ,of x+12x2n is

The middle term in the expansion ,of ${(x + \frac{1}{2 x})}^{2 n} is$

A
$\frac{1 \cdot 3 \cdot 5 \dots (2 n - 3)}{n!}$
B
$\frac{1 \cdot 3 \cdot 5 \dots (2 n - 1)}{n!}$
C
$\frac{1 \cdot 3 \cdot 5 \dots (2 n + 1)}{n!}$
D
None of the above

Solution:

Given expression is ${(x + \frac{1}{2 x})}^{2 n}$

$\begin{aligned} ∴ Middle term =^{2 n} C_{n} (x)^{n} {(\frac{1}{2 x})}^{n} \\ = \frac{2 n!}{n! n! 2^{n}} = \frac{1 \cdot 3 \cdot 5 \dots (2 n - 1)}{n!} \end{aligned}$

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