## If z is one of the roots of unity with index n, find the sum

1. The problem statement, all variables and given/known data
Given the fact that z is one of the n-th roots of unity, find the sum below:
1 + 2z + 3z2 + ... + nzn-1

2. Relevant equations

(1-x)(1+x+...+xn-1) = 1 - xn

3. The attempt at a solution
honestly I don't know how to do this. any help is appreciated

 PhysOrg.com science news on PhysOrg.com >> Hong Kong launches first electric taxis>> Morocco to harness the wind in energy hunt>> Galaxy's Ring of Fire
 ..the hint for the solution is called complete induction. ;) First of all you starting to show that the beginning of the sequence is true. After that you show that its also true for n+1... Try to make some sort of attempt to solve it...
 Divide eqn 2 with (1-x) and try solvin it using some calculus

## If z is one of the roots of unity with index n, find the sum

Yes u can use induction also. But try solving it using calculus. It is simpler and more intrestring

 what I'm trying to solve is this 1 + 2z + 3z2 + ... + nzn-1
 Recognitions: Gold Member Science Advisor Staff Emeritus Yes, you said that initially and you have two different suggestions as to how to do that. Have you tried either?
 I don't know how to apply induction to a sum. there is no "=" to prove. I have to find the sum, not prove something given. That's why I don't know how to apply induction.

 Quote by tonit 2. Relevant equations (1-x)(1+x+...+xn-1) = 1 - xn
There is one relevant eqn missing

Recognitions:
Homework Help
 Quote by tonit I don't know how to apply induction to a sum. there is no "=" to prove. I have to find the sum, not prove something given. That's why I don't know how to apply induction.
I'm guessing that you're supposed to find a formula for the series (without 3 dots in it).

 Recognitions: Homework Help Science Advisor Hint: What do you get if you differentiate x+x^2+...+x^n?