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Summation Confusion

  1. Sep 5, 2009 #1
    1. The problem statement, all variables and given/known data

    This is kind of a question regarding summation.

    All logs are to base 2.

    Given

    [tex]A=\sum_{n=2}^{\infty}(n\log^{2}(n))^{-1}[/tex]

    Why does the the Author get

    [tex]\sum_{n=2}^{\infty}\frac{\log A}{An\log^{2}(n)}=\log A[/tex]
    ?



    2. Relevant equations



    3. The attempt at a solution

    But working it out, I get

    [tex]\sum_{n=2}^{\infty}\frac{\log A}{\sum_{n=2}^{\infty}(n\log^{2}(n))^{-1}n\log^{2}(n)}=\sum_{n=2}^{\infty}\frac{\log A}{\sum_{n=2}^{\infty}1}[/tex]

    Since [tex]A\approx1.013[/tex]

    [tex]log(A)\approx0.019[/tex]

    Therefore

    [tex]\sum_{n=2}^{\infty}\frac{0.019}{\infty}=0[/tex]

    What did I do wrong?

    Thanks for any help in advance.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 5, 2009 #2
    A is already a summed expression. Therefore, you can pull it out of the sum:
    [tex]\frac{logA}{A} \Sigma \left( n \log^2(n) \right)^{-1}[/tex], which is (logA/A)*A=logA.
     
  4. Sep 5, 2009 #3

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Too much help there, javier. A hint to pull a constant factor out of the sum would have been enough.
     
  5. Sep 5, 2009 #4
    That was perfect thanks :)
     
    Last edited: Sep 5, 2009
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