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The coefficient of x^(2012) in (1x)/((1+...

The coefficient of `x^(2012)` in `(1_x)/((1+x^(2))(1-x))` is -

A

2010

B

2011

C

2012

D

2013

Text Solution

Verified by Experts

The correct Answer is:
B
Coeff. Of `x^(2012)`
`((1+x))/((1+x^(2))(1-x^(2)))`
`=(1+x^(2))(1-x^(4))^(-1)`
`=(1+2x+x^(2))(1-x^(4))^(-1)`
Coeff. Of `x^(2012)+2"Coeff of x"^(2011)+"Coeff of x"^(2010)` in the expansion of `(1-x^(4))^(-1)`
`x^(2011) and x^(2010)` not possible in `(1-x^(4))^(-1)`
= only coeff. of `x^(2012)` in the expassion of `(1-x^(4))^(-1)`
`.^(1+503-1)C_(503)=1`
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