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Help finding the behaviour of this series?

  1. Apr 13, 2009 #1
    given the following series and i am asked if it converges or diverges in its boundaries

    0 + ln(2)/4 + ln(3)/9 + ln(4)/16 + ...... + ln(n)/n^2

    to find out if series converge/diverge, i have been using comparisons, finding a similar series, B(n) whose behaviour i know or can easily find, then saying :
    # if B(n) > A(n), and B(n) converges, then A(n) converges
    # if B(n) < A(n), and B(n) diverges, then A(n) diverges
    # if A(n)/B(n)=K (K= not 0, not ∞) then A(n) and B(n) behave the same

    but i cannot find any series that answers to any of these 3 condidtions, any ideas? the series must either have a known or relatively simple to find behaviour.
     
  2. jcsd
  3. Apr 13, 2009 #2

    king vitamin

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    Gold Member

    Finding the convergence of series involving logs can be tough because it can be hard to see how log behaves in comparison to polynomials. To get a good sense of this, try graphing in the same window y=ln(x) along with some polynomials such as y=x, y=x^(1/2), y=x^(1/5), etc. What you should generally find is that all x^a (with a > 0) is less than ln(x) for large x. This should help you find a convergent polynomial series greater than yours.
     
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