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Homework Help: Finding the sum of an infinite series

  1. Jun 22, 2011 #1
    1. The problem statement, all variables and given/known data
    I am supposed to find the value of the infinite series:


    2. Relevant equations

    I asked this question before on this forum and micromass told me that I should use cos(n)=((e^i)^n+(e^(-i))^n)/2. That equation worked and I was able to find the correct answer. I used that equation to find a "a" and an "r" in order to find the solution using =a/(1-r).

    But my instructor said he would like me to try and solve it by only using real numbers.

    How would I start to solve that without the imaginary numbers?

    Last edited: Jun 22, 2011
  2. jcsd
  3. Jun 22, 2011 #2


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    Homework Helper

    just an idea, but how about considering angle sum formulas...
    ie what is
    in terms of only n?
  4. Aug 7, 2011 #3


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    Science Advisor
    Homework Helper

    try multiplying by cos(1) …

    S*cos(1) = ∑ π cos(n)cos(1)/5n = … ? :wink:
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