If alpha is the nth root of unity then 1...

If `alpha` is the nth root of unity then `1+2alpha+3alpha^(2)+`............to `n` terms is equal to

A

`(2n)/(1-alpha)`

B

`-(2n)/(1-alpha)`

C

`(n)/(1-alpha)`

D

`-(n)/(1-alpha)`

Verified by Experts

Similar Questions

Explore conceptually related problems

If alpha is a non-real fifth root of unity, then 3^(|1+alpha+a^(2)+a^(-2)-a^(-1) |)=

If alpha and beta are non real cube roots of unity then alpha beta+alpha^(5)+beta^(5)=

If alpha is an imaginary fifth root of unity then log _(2)|1+alpha+alpha^(2)+alpha^(3)-(1)/(alpha)|=

If alpha is a non-real fourth roots of unity, then the values of alpha^(4 n-1)+alpha^(4 n-2)+alpha^(4 n-3), n in N is

If alpha and beta are the roots of x^(2) - ax + b^(2) = 0, then alpha^(2) + beta^(2) is equal to :

If alpha is an imaginary root of the equation z^(n)-1=0 then 1+alpha+alpha^(2)+….. .+alpha^(n-1)=

If alpha and beta are the roots of x^(2)-ax+b^(2)=0 , then alpha^(2) +beta^(2) is equal to_______

If alpha and beta are the roots of x^(2)+x+1=0 , then alpha^(16)+beta^(16)=

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.