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Question: The co-efficient of the middle term in the expansion of (1+x)<sup>2n</sup> is...

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

A

2 nCn

B

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

C
    1. …. (4n – 2)
D

None of these

Answer

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

Explanation

Solution

Coefficient will be2nCn=2n!(n!)22nC_{n} = \frac{2n!}{(n!)^{2}}

= 1.3.5⋯(2n−1).2.4.6.8⋯2n(n!)2\frac{1.3.5\cdots(2n - 1).2.4.6.8\cdots 2n}{(n!)^{2}}= 1.3.5⋯(2N−1)N!⋅2n\frac{1.3.5\cdots(2N - 1)}{N!} \cdot 2^{n}