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Homework Help: Determine if series converges

  1. May 17, 2010 #1
    1. The problem statement, all variables and given/known data

    Is the series convergent

    1) [tex]\sum[/tex]1/(n^2 * ln n)

    and 2) which value of p does the series converge. [tex]\sum[/tex] 1/(n*(ln n)^p)

    3. The attempt at a solution


    I cannot see how the root method ([tex]\sqrt[n]{Cn}[/tex]) would work, or the ratio test would work (cn+1)/cn

    Unless you use the limit test and lim 1/(n^2 * ln n) = 1/infinity = 0 therefore the series converges. I didnt think that question would be that easy though.

    2) Similiar to the first wouldn't it just be if P > 1.
  2. jcsd
  3. May 17, 2010 #2


    Staff: Mentor

    The test you are thinking of, I believe, is the nth term test for divergence. If lim an != 0, the series diverges. You cannot use this test to conclude a series converges.

    A test that might be useful in this problem is the comparison test.
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