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Question

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

A
2nCn
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B
1.3.5..(2n1)n!2n
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C
2.6(4n2)
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D
2.42n
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Solution

The correct options are
A 2nCn
B 1.3.5..(2n1)n!2n
Middle term =N2+1

=2n2+1

=(n+1)thterm

Now consider the following

Tr+1=nCranrbr...(i)

Where T represents the term.

Here the middle term is the (n+1)th term

Hence r+1=n+1

r=n

substituting in (i), we get

2nCn12nnxn

=2nCnxn

Hence the coefficient of middle term is 2nCn which can also be written as

(1.3.5...(2n1))2nn!

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