1. Limited time only! Sign up for a free 30min personal 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!

Sum of complex series

  1. Mar 8, 2010 #1
    1. The problem statement, all variables and given/known data

    Given that Wn = 3-n cos 2nӨ for n = 1, 2, 3, …, use de Moivre’s theorem to show that

    1 + W1 + W2 + W3 + … + WN-1 = [ 9 – 3 cos2Ө+ 3-N+1 cos2(N-1)Ө - 3-N+2 cos2NӨ] / [10 – 6cos2Ө]

    Hence show that the infinite series
    1 + W1 + W2 + W3 + …
    is convergent for all values of Ө, and find the sum to infinity

    Please i need help on how to solve this above question. though I have posted it before in my blog but was deleted. I don't know the reason for the deletion. I guessed I should have posted it in homework section

    2. Relevant equations

    3. The attempt at a solution
    I don't have a clue to this question, I have tried to use A.P and G.P formulas but proved difficult. I need help in order to teach my students preparing for external exams in further maths.
  2. jcsd
  3. Mar 8, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Wn will be the real part of [tex]3^{-n}e^{2n\theta i}[/tex]. So summing up Wns is the same thing as taking the real part of a geometric series of terms like that.
  4. Mar 9, 2010 #3
    I have used ur suggestion,as follows common ration = 3-1 e2Өni, first term = 1, however I got stucked.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook