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Math Help - determining whether a series converges absolutely

  1. #1
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    determining whether a series converges absolutely

    Determine whether the series (-1)k-11/3k2+2k+1 converges absolutely, converges conditionally, or diverges. (and the summation goes to infinity and starts at k=1).
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  2. #2
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    Re: determining whether a series converges absolutely

    Since

    \left\lvert (-1)^{k-1}\frac{1}{3k^2+2k+1} \right\rvert = \frac{1}{3k^2+2k+1}< \frac{1}{3k^2}

    you can use the comparison test, right?
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  3. #3
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    Re: determining whether a series converges absolutely

    Yes, and obviously it converges. So it would converge absolutely?
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  4. #4
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    Re: determining whether a series converges absolutely

    The series of absolute values converges, so the original series converges absolutely.

    - Hollywood
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