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If ,Z1,Z2,Z3,........Z(n-1) are n^(th) ...

If `,Z_1,Z_2,Z_3,........Z_(n-1)` are `n^(th)` roots of unity then the value of `1/(3-Z_1)+1/(3-Z_2)+..........+1/(3-Z_(n-1))` is equal to

A

`(n.3^(n-1))/(3^(n)-1)+1/2`

B

`(n.3^(n-1))/(3^(n)-1)-1`

C

`(n.3^(n-1))/(3^(n)-1)+1`

D

`(n.3^(n-1))/(3^(n)-1)-1/2`

Text Solution

Verified by Experts

The correct Answer is:
D
`z^(n)-1=(z-1)(z-z_(1))(z-z_(2))……(z-z_(n-1))`
take log and differentiate both side and then put `z=3`
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