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Series question

  1. Nov 14, 2006 #1
    Hi, I just wondering if someone can help me on this question.

    1) 1/(n(ln n ) ^p)

    2) 1/((n(ln n)(ln (ln n))))^p

    Both are b = infinity and a = 1 for the integral signs.

    The question is for what value of p>0 does the series converges and for what value does it diverges.

    Thank you !!!
  2. jcsd
  3. Nov 14, 2006 #2


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    Homework Helper

    There was a similar question in the HW section recently. Use the integral test.
  4. Nov 14, 2006 #3


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    Do you know about the criterion [itex]\sum a_n[/itex] converges iff [itex] \sum 2^n a_{2^n}[/itex] converges? It is usefull for series involving ln(n) because ln(2^n)=nln(2) !

    Then, for the values of p, use the ratio test (a_{n+1}/a_n).
    Last edited: Nov 14, 2006
  5. Nov 14, 2006 #4


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    It's important to keep in mind this only works when the series is monotonically decreasing (which this one is). Otherwise, just take the terms to be all 1's except for 0's when n is a power of 2.
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