The middle term in the expansion of ( 1 + x ) 2 n is Options: A . &nbsp 1.3.5....... ( 5 n − 1 ) n ! x n B . &nbsp 2.4.6.......2 n n ! x 2 n + 1 C . &nbsp 1.3.5....... ( 2 n − 1 ) n ! x n D . &nbsp 1.3.5....... ( 2 n − 1 ) n ! 2 n x n

Answer: Option D : D Middle term of ( 1 + 2 x ) 2 n is T n + 1 = 2 n C n x n = ( 2 n ) ! n ! n ! x n = 1.3.5....... ( 2 n − 1 ) n ! 2 n x n .

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

Question -

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

Options:

A .

\frac{1.3.5....... (5 n - 1)}{n!}

x^{n}

B .

\frac{2.4.6.......2 n}{n!}

x^{2 n + 1}

C .

\frac{1.3.5....... (2 n - 1)}{n!}

x^{n}

D .

\frac{1.3.5....... (2 n - 1)}{n!}

2^{n} x^{n}

Answer: Option D
:
D

Middle term of $(1 + 2 x)^{2 n}$ is $T_{n + 1}$ = $^{2} n C_{n}$ $x^{n}$

= $\frac{(2 n)!}{n! n!}$ $x^{n}$ = $\frac{1.3.5....... (2 n - 1)}{n!}$ $2^{n}$ $x^{n}$ .

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