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!

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


    User Avatar
    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


    User Avatar
    Science Advisor
    Homework Helper

    try multiplying by cos(1) …

    S*cos(1) = ∑ π cos(n)cos(1)/5n = … ? :wink:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook