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Homework Help: 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


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    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

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    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


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    Homework Helper

    Hint: What do you get if you differentiate x+x^2+...+x^n?
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