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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`.

4 views Answered 2023-02-05 15:29