1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Apr 8, 2012 #1
    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
     
    Last edited: Apr 8, 2012
  2. jcsd
  3. Apr 8, 2012 #2
    ..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...
     
  4. Apr 8, 2012 #3
    Divide eqn 2 with (1-x) and try solvin it using some calculus
     
  5. Apr 8, 2012 #4
    Yes u can use induction also. But try solving it using calculus. It is simpler and more intrestring
     
  6. Apr 8, 2012 #5
    what I'm trying to solve is this
    1 + 2z + 3z2 + ... + nzn-1
     
  7. Apr 8, 2012 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, you said that initially and you have two different suggestions as to how to do that. Have you tried either?
     
  8. Apr 10, 2012 #7
    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.
     
  9. Apr 10, 2012 #8
    There is one relevant eqn missing
     
  10. Apr 10, 2012 #9

    I like Serena

    User Avatar
    Homework Helper

    I'm guessing that you're supposed to find a formula for the series (without 3 dots in it).
     
  11. Apr 10, 2012 #10

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Hint: What do you get if you differentiate x+x^2+...+x^n?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: If z is one of the roots of unity with index n, find the sum
  1. Roots of unity (Replies: 1)

  2. N-th root of unity (Replies: 3)

  3. Roots of unity (Replies: 9)

Loading...