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Series Test for convergent and divergent

  1. Apr 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Ʃ √n/(ln(n))^2
    from n=2 to ∞


    2. Relevant equations

    Series Test for convergent and divergent

    3. The attempt at a solution

    I tried doing ratio test and gotten
    [√(n+1)*(ln(n))^n] / [(ln(n+1))^(n+1) * √n]

    to find the limit, do i cont by using Hopstal rule?
     
  2. jcsd
  3. Apr 17, 2013 #2

    Mark44

    Staff: Mentor

    That is not correct. It should be
    $$ \frac{\sqrt{n+1}~(ln(n))^2}{\sqrt{n}~(ln(n+1))^2}$$

    In any case, I don't think the Ratio Test is going to be much help here. What other tests do you know?
     
  4. Apr 17, 2013 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The absolute first check you should always make is to check that the nth term approaches 0. l'Hopital's should help there.
     
  5. Apr 17, 2013 #4
    I made a mistake in the question its suppose to be power of n

    Ʃ √n/(ln(n))^n
    from n=2 to ∞

    I have learnt root test, integral test, comparison and limit test.

    however I do not see how these will help solve this question.
     
  6. Apr 17, 2013 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's little more subtle. Can you show (ln(n))^n will eventually dominate any power series? For example, (ln(n))^n>n^2 for sufficiently large n? That would let you make a comparison test.
     
  7. Apr 18, 2013 #6
    Oh. thanks for the tip. I gona try it rite now. Thanks
     
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