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Summation of a Logarithmic Series

  1. Jul 10, 2012 #1


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    1. The problem statement, all variables and given/known data
    What is the sum of the following series?


    Where log(x) is log base 10 of x.

    2. Relevant equations

    3. The attempt at a solution
    Evidently, the previous form equals:


    I'm missing something - no patterns are evident to me other than the denominator and numerator of the subsequent terms cancel out.

    Any guidance would be appreciated.
  2. jcsd
  3. Jul 10, 2012 #2


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    And that's important! What are you left with after cancelling *everything* that can be cancelled?
  4. Jul 10, 2012 #3

    Do you see in what pattern the terms cancel and which terms are left? :wink:
  5. Jul 10, 2012 #4


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    Intuitively, yes - would it be correct in saying that all terms cancel other than 1/2 and 200/1, leaving 200/2?
  6. Jul 10, 2012 #5


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    Yes, that would be correct, and you didn't find it intuitive even though you spotted the pattern?
  7. Jul 10, 2012 #6
    Yes, only 1/2 and 200/1 remains. 3 cancels 1/3, 4 cancels 1/4, 5 cancels 1/5 but there's no one to cancel 200 and 1/2.
  8. Jul 10, 2012 #7


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    Quickly edited after rereading :frown:. I'm not sure why I didn't recognize that pattern before.
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