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For what values of x does this series converge

  1. Apr 1, 2007 #1
    1. The problem statement, all variables and given/known data
    Series is:

    (ln x)^n, n goes from 1 to infinity

    2. Relevant equations

    3. The attempt at a solution
    For other problems I've seen the ratio test used to find the radius of convergence, but I don't think this can work here. What other things can I do to find where this converges?
  2. jcsd
  3. Apr 1, 2007 #2
    For what values of x does the series:


    Last edited: Apr 1, 2007
  4. Apr 2, 2007 #3


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    Staff Emeritus
    Science Advisor

    Why wouldn't the ratio test work here? The ratio test, remember, works for every infinite series, not just power series.
    [tex]\frac{(ln x)^n}{(ln x)^{n+1}}= \frac{1}{ln x}[/tex]
    In order that the series converge, that fraction must be less than 1.

    (And, of course, that gives the same answer as mattmns' solution.)
    Last edited: Apr 2, 2007
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