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The coefficient of x^n in the expansion ...

The coefficient of `x^n` in the expansion of `(1-x)(1-x)^n` is `n-1` b. `(-1)^n(1-n)` c. `(-1)^(n-1)(n-1)^2` d. `(-1)^(n-1)n`

A

`(-1)^(n-1) n`

B

`(-1)^(n) (1 -n)`

C

`(-1)^(n-1) (n-1)^(2)`

D

`(n -1)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have ,
Coefficient of `x^(n)` in `(x +n) (1 - x)^(n)`
Coefficent of `x^(n)` in `(1 - x)^(n)` + Coefficient of `x^(n-1)` in `(1 -x)^(n)`
`= (-1)^(n) ""^(n)C_(n) + (-1)^(n -1) ""^(n) C_(n-1) = (-1)^(n)(1 -n)`
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