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Series and convergence/divergence

  1. Feb 29, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine whether the series converges:

    \sum\limits_{n = 2}^{\inf } {\frac{{( - 1)^n (n^2 + 1)^{1/2} }}{{n\ln (n)}}}

    3. The attempt at a solution

    Which test must I use? I thought of using the integral test, but it seems a little too hard. Are there other possibilities?
  2. jcsd
  3. Feb 29, 2008 #2
    Try either the ratio or root test. Neither would be very easy to calculate, but...
  4. Feb 29, 2008 #3


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    Well, the [itex](-1)^n[/itex] should give you an easy test...

    BTW: \infty is [itex]\infty[/itex]
  5. Feb 29, 2008 #4
    Should I just take:

    \sum\limits_{n = 2}^{\inf } {\frac{{( - 1)^n (n^2 + 1)^{1/2} }}{{n\ln (n)}}}^{(1/n)}
    [/tex] and take the limit of this?
  6. Feb 29, 2008 #5
    Its an alternating series, what about the Leibinitz test?
  7. Mar 1, 2008 #6
    I looked at the Leinitz test - on wikipedia they write about the first condition:

    "If the sequence a_n converges to 0, and .." - does this mean the limit of a_n for n -> infinity?
    Last edited: Mar 1, 2008
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