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Coefficient of x^(2009) in (1+x+x^(2)+x^...

Coefficient of `x^(2009)` in `(1+x+x^(2)+x^(3)+x^(4))^(1001) (1-x)^(1002)` is

A

`0`

B

`4."^(1001)C_(501)`

C

`-2009`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `(1+x+x^(2)+x^(3)+x^(4))^(1001)(1-x)^(1002)`
`((1-x^(5))/(1-x))^(1001)(1-x)^(1002)=((1-x)(1-x^(5)))^1001`, so all the powers of `x` will be of the `5m` or `5m+1(m in I)`
So coefficient of `x^(2009)` will be `0`
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