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Sum of the convergent infinite series ln(n)/n^2

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the sum of the series: ln(n)/n^2 from n=1 to infinity.
    I already know that it is convergent(at least i hope i am right on that fact)

    2. Relevant equations



    3. The attempt at a solution
    I tried to use geometric series but i can't see anything like that that would work, and i can't see a way to use telescoping. And just starting with n=1 and summing numbers didn't seem to get me anywhere either.
     
  2. jcsd
  3. Jan 22, 2009 #2
    You still can use telescoping.
    ln((n+1)^(1/(n+1)^2))-ln(n^(1/n^2)), use stolz theorem on this limit to get your answer, btw I am sure you know that but stolz theorem resembles L'hopital theorem.
     
  4. Jan 27, 2009 #3
    Thank you very much :)
     
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