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Infinite Series with log natural Question

  1. Apr 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Ʃ (-1)^(k+1) / kln(k)
    k=2

    2. Relevant equations
    integral test, p test, comparison test, limit comparison, ratio test, root test.


    3. The attempt at a solution
    In class so far we have not learned the alternating series test so i can't use that test.
    So far I have done the test for divergent which turned up 0, ratio test which turned up 1, root test which didn't work, and its not a geometric or telescoping series.
    I think that the only one that will work is the comparison test but I don't know what to use to compare this function.
     
  2. jcsd
  3. Apr 5, 2013 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    From your question I gather that you only need to say whether the series converges, not what the limit is.

    Never mind my old post, it doesn't seem to help.

    [old post]
    I am not sure how much you have and haven't seen, but one common approach would be looking at the absolute value and using the triangle inequality to write

    [tex]\left| \sum_{k = 2}^\infty \frac{(-1)^{k + 1}}{k \ln k} \right| \le \sum_{k = 2}^\infty \left| \frac{(-1)^{k + 1}}{k \ln k} \right|[/tex]

    It may also be useful to note that ln k > 1 for k > 2.
    [/old post]


    [new hint]
    Whichever way you try the comparison test, it will always end up "going the wrong way".
    Try an integral test instead.
     
    Last edited: Apr 5, 2013
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