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If f(x)=1-x+x^2-x^3++^(15)+x^(16)-x^(17)...

If `f(x)=1-x+x^2-x^3++^(15)+x^(16)-x^(17)` , then the coefficient of `x^2 in f(x-1)` is `826` b. `816` c. `822` d. none of these

A

826

B

816

C

822

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x) = 1-x+x^(2)-x^(3)+"……"-x^(15)+x^(16)-x^(17)= (1-x^(18))/(1+x)`
`rArr f(x-1)= (1-(x-1)^(18))/(x)`
Therefore, required coefficient of `x^(2)` is equal to coefficient of `x^(3)` in `1-(x-1)^(18)`, which is given by `.^(18)C_(3)=816`.
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