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Homework Help: Test for conver

  1. Feb 18, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\sum(\frac{1}{\sqrt{ln k +2}-\sqrt{ln k -2})}k[/tex]
    as k [tex]\rightarrow[/tex][tex]\infty[/tex]

    2. Relevant equations
    Root test: (ak)1/k


    3. The attempt at a solution
    (ak)1/k = (\frac{1}{\sqrt{ln k +2}-\sqrt{ln k -2})
    does it equal 0? since 1/[tex]\infty[/tex] = 0
    but its [tex]\infty[/tex] - [tex]\infty[/tex] i would have to use l'Hôpital's rule right?
     
  2. jcsd
  3. Feb 18, 2009 #2

    Tom Mattson

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    No, I would rationalize the denominator. L'Hopital won't be necessary.
     
  4. Feb 18, 2009 #3
    Then i would get

    [tex]\frac{\sqrt{ln k + 2} + \sqrt{ln k - 2}}{4}[/tex]

    as k approaches infinity, the function would also approach infinity so it diverges?
     
  5. Feb 18, 2009 #4

    Tom Mattson

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    That's what I got.
     
  6. Feb 18, 2009 #5
    thanks
     
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