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Homework Help: Double Sum

  1. Jan 30, 2010 #1
    1. The problem statement, all variables and given/known data

    What is [tex]\sum_{n=0}^{\infty} (-1)^n\sum_{k=0}^{n} n!/(n-k)!* ln^{n-k}(2)[/tex]?

    2. Relevant equations



    3. The attempt at a solution
    How to work with the double sum?
     
  2. jcsd
  3. Jan 30, 2010 #2
    Could I combine the two sums into one? I am not sure how, but I have a feeling that is what I am supposed to do. Thanks.
     
  4. Jan 30, 2010 #3

    Mark44

    Staff: Mentor

    I don't think you can, but I could be wrong.

    I would start expanding it and see if that gets me anywhere. One thing that bothers me is that you will have numerous expressions with ln0(2). I don't know what that means, but maybe it's supposed to represent just plain 2.

    If you start expanding the double sum, you get:
    (+1)*( 2) ; n = 0
    + (-1)*(1!/1! * ln(2) + 1!/0! * 2) ; n = 1, k = 0, k = 1
    + (+1)*(2!/2! * ln2(2) + 2!/1! * ln(2) + 2!/0! * 2) ; n = 2, k = 0, 1, 2
    and so on.
     
  5. Jan 30, 2010 #4
    I am getting that the sum goes to infinity- is this right?
     
  6. Jan 31, 2010 #5

    Mark44

    Staff: Mentor

    Looks that way to me. The limit of the nth term of the series isn't zero, so the series diverges.
     
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