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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:

    [tex]\sum_{n=0}^{+\infty}\frac{\pi\cos(n)}{5^n}[/tex]

    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?

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

    lanedance

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    Homework Helper

    just an idea, but how about considering angle sum formulas...
    ie what is
    cos(n)
    cos(2n)
    cos(3n)
    in terms of only n?
     
  4. Aug 7, 2011 #3

    tiny-tim

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    Science Advisor
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    try multiplying by cos(1) …

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