nth roots of Unity

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

If omega is a complex nth root of unity, then underset(r=1)overset(n)(ar+b)omega^(r-1) is equal to

If alpha(!=1) is a nth root of unity then S=1+3 alpha+5 alpha^(2)+......... upto n terms is equal to

If alpha is the nth root of unity then prove that 1+2 alpha+ 3 alpha^2+…. upto n terms

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

If omega is a complex nth root of unity, then underset(r=1)overset(n)(ar+b)omega^(r-1) is equal to

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

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