complex number

Question

IF 1,ω+ω²+.....+ω^n-1 are the n^th root of unity, then the value of (1/x-1)+(1/x-ω) +......+1/x-ω^n-1 =________?

 

Answer 1

I just did the cube roots of 1 and the fourth roots of 1 and it looks like your answer is going to be that the sum is

 

n*x^(n-1) / (x^n - 1)

 

For the cube roots it came out to be 3x^2 / (x^3 - 1) 

For the fourth roots it came out to be 4x^3 / (x^4 - 1) 

 

Just because this looks like the general pattern, doesn't mean it's right. Working on a proof for this.