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Math Help - Can you use the alternating test to conclude if a series is divergent?

  1. #1
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    Can you use the alternating series test to conclude if a series is divergent?

    If an infinite series is not monotonically decreasing and if it does not approach 0 but instead approaches infinity, would this be sufficient information to conclude that the series is divergent since it doesn't meet the alternating test's requirements?
    Last edited by MathIsOhSoHard; October 13th 2012 at 07:38 PM.
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    Re: Can you use the alternating test to conclude if a series is divergent?

    Hey MathIsOhSoHard.

    Can you outline the example you are talking about?
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    Re: Can you use the alternating test to conclude if a series is divergent?

    Quote Originally Posted by chiro View Post
    Hey MathIsOhSoHard.

    Can you outline the example you are talking about?
    \sum^\infty_{n=1}(-2)^n\frac{1}{n^2+7}

    Then:
    a_n=\frac{2^n}{n^2+7}

    This does not decrease monotonically nor does it approach zero, so would I be able to conclude that it is divergent based on the alternating series test? Or would the test be inconclusive and I'd have to use another test?
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    Re: Can you use the alternating test to conclude if a series is divergent?

    The nth term test should show that this diverges as long as n > 4 so you can break up the series with n = 1 to 4 and then another series with n = 4 onwards and show that absolute value is greater than 1 for all terms which means it diverges.
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