In the expansion of [(1+x)//(1-x)]^2, th...

In the expansion of `[(1+x)//(1-x)]^2,` the coefficient of `x^n` will be a.`4n` b. `4n-3` c. `4n+1` d. none of these

A

`4n`

B

`4n-3`

C

`4n+1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

A

Given term can be written as
`(1+x)^(2)(1-x)^(-2)=(1+2x+x^(2))[1+2x+3x^(2)+"....."+(n-1)xxx^(n-2)+nx^(n-1)+(n+1)x^(n)+"...."oo]`
Coefficient of `x^(n)` is `(n+1+2n+n-1)=4n`.

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