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Integral test

  1. Sep 25, 2009 #1
    1. The problem statement, all variables and given/known dataDetermine convergence or divergence using the integral test for.
    [tex]\sum _{x=2}^{\infty } \left( \ln \left( x \right) \right) ^{-1}[/tex]



    2. Relevant equationsi should take the limit as b goes to infinity of

    [tex]\int _{2}^{b}\! \left( \ln \left( x \right) \right) ^{-1}{dx}[/tex]

    The problem is that the function is not integrable.I know there was trick show that it is divergent but I don't remember what it was.
    3. The attempt at a solution
     
    Last edited: Sep 25, 2009
  2. jcsd
  3. Sep 25, 2009 #2

    LCKurtz

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    When you say it isn't integrable, do you mean the integral diverges or that you can't find an antiderivative?

    The integral and the series converge or diverge togther.
     
  4. Sep 25, 2009 #3
    I cant find the antiderivative. Maple give's me [tex]-{\it Ei} \left( 1,-\ln \left( x \right) \right) [/tex] and i don't know what it means. I am currently doing cal 3 but I think remember this exercise from cal 2. Is there any other test that I could use to show the divergence?
     
  5. Sep 25, 2009 #4
    I would do a comparison with 1/√x.
     
  6. Sep 25, 2009 #5
    ln(2n) = n*ln(2) < n so 1/ln(2n) > 1/n if that helps.
     
  7. Sep 25, 2009 #6
    Thanks. It is divergent by the comparison test.
     
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