If $$1$$,ω,.....ω$$n-1$$ are the nth roots of unity, then value of $$12-$$ω$$+12-$$ω$$2+$$...$$+12-$$ω$$n-1$$ equals

Correct option is 4none of these

Questions

If $1, ω, . . . . . ω^{n - 1}$ are the nth roots of unity, then value of $\frac{1}{2 - ω} + \frac{1}{2 - ω^{2}} + . . . + \frac{1}{2 - ω^{n - 1}}$ equals

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12n-1

n(2n-1)2n+1

(n-2)2n-12n-1

none of these

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detailed solution

Correct option is D

We know that1x−1+1x−ω+1x−ω2+⋯+1x−ωn−1=nxn−1xn−1Putting x=2, we get 12−ω+12−ω2+⋯+12−ωn−1=n2n−12n−1

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If 1,ω,.....ωn-1 are the nth roots of unity, then value of 12-ω+12-ω2+...+12-ωn-1 equals

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If $1, ω, . . . . . ω^{n - 1}$ are the nth roots of unity, then value of $\frac{1}{2 - ω} + \frac{1}{2 - ω^{2}} + . . . + \frac{1}{2 - ω^{n - 1}}$ equals