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Math Help - Convergence problem

  1. #1
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    Convergence problem

    Determine whether the series converges absolutely, converges conditionally or diverges:

    (The sum as k > infinity) (-1)^k+1 (1/((k^3) - 1))

    This test is inconclusive on the ratio test for abs. convergence and I'm not certain it can be used with the alternating series test because a1=0.

    Can anyone help me out here?
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  2. #2
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    Anyone know what to do here?
    I'm trying the integral test, but I'm not sure how to integrate:

    1
    -------
    k^3 - 1
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  3. #3
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    Quote Originally Posted by TripleHelix View Post
    Determine whether the series converges absolutely, converges conditionally or diverges:

    (The sum as k > infinity) (-1)^k+1 (1/((k^3) - 1))

    This test is inconclusive on the ratio test for abs. convergence and I'm not certain it can be used with the alternating series test because a1=0.

    Can anyone help me out here?
    First compare the series \sum_{k = 2}^{\infty} \frac{1}{k^3-1} with \sum_{k = 2}^{\infty} \frac{1}{k^3} (limit comparison test) to check for absolute convergence.
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