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Series - help.

  1. Nov 2, 2007 #1
    I am trying to practice for an exam but can't do this question:

    does the series [tex]\((-1)^n/ln(n)[/tex] from n = 2 to infinity converge abs/conditionally/diverge?

    I know if a do an alternating series test, the integral will converge because lim goes to 0 and a(n+1)<an.

    But how can I prove that it's conditionally convergent? I did the limit test but it says that it is absolutely convergent, which is not the answer(it is supposed to be conditionally).

    Thank you...
    Last edited: Nov 2, 2007
  2. jcsd
  3. Nov 3, 2007 #2

    Gib Z

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    Homework Helper

    Well it can't be absolutely, because 1/( ln n ) goes to 0 much slower than another well known series that diverges doesn't it?
    Last edited: Nov 3, 2007
  4. Nov 3, 2007 #3
    ok, 1/n diverges as is a bigger series, so 1/ln(n) must also converge, right?
  5. Nov 3, 2007 #4
    write it with inequalities and using the definition of "diverge" show that 1/n FORCES 1/lnn to blow up.
  6. Nov 3, 2007 #5
    Sorry I meant, since thesmaller series diverges, 1/ln(n) will also diverge.
  7. Nov 3, 2007 #6


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    Staff Emeritus
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    And since 1/ln n is a decreasing sequence, the "conditional convergence" part is easy!
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