If `alpha` is an `n^(th)` roots of unity, then `1+2alpha+3alpha^(2)+……..+nalpha^(n-1)` equals

If alpha is an n^(th) root of unity then prove that 1+2alpha+3alpha^2+4alpha^3+….+nalpha^(n-1)=-(n)/(1-alpha)

If 'alpha' be the non-real n^(th) roots of unity, then 1+3alpha+5alpha^2+…...(2n-1)alpha^(n-1) is equal to

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

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

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

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

If 1,alpha,alpha^2,…...,alpha^(n-1) are the n^(th) roots of unity, then the value of (3-alpha)(3-alpha^2)…...(3-alpha^(n-1)) is

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

If 1,alpha,alpha^(2),......alpha^(n-1) are n,n^(th) roots ofunity, then 1+2 alpha+3 alpha^(2)+4 alpha^(3)+......+n terms is equal to