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Convergence and Sum of Series

  1. Nov 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Please write a specific function to define this series. Also provide a sum that the series converges to.


    2. Relevant equations

    Sn - {1, 1+1/e2, 1+1/e2+1/e4, 1+1/e2+1/e4+1/e6, ...}

    3. The attempt at a solution

    I know that the common ratio is 1/e2 and that you can raise that to the nth exponent for the last portion of each term, but how would I write this along with the previous parts from n-1, n-2, n-3, etc. added to it for each term? In other words, how can I show this in sigma notation and find the sum of it?

    Thanks,
    Dane
     
  2. jcsd
  3. Nov 3, 2012 #2

    micromass

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    What do you know about geometric sequences?? Do you know how to find the sum of one?
     
  4. Nov 3, 2012 #3
    I believe it is a1/1-r, so 1/1-(1/e^2)? But I need to know how to express this in sigma notation first. I can't figure out how to represent it.
     
  5. Nov 3, 2012 #4
    Anyone?
     
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