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Math Help - Match each of the following with the correct statement #2

  1. #1
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    Match each of the following with the correct statement #2

    Match each of the following with the correct statement.
    A. The series is absolutely convergent.
    C. The series converges, but is not absolutely convergent.
    D. The series diverges.

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    Last edited by mr fantastic; May 19th 2010 at 12:34 AM. Reason: Edited post title.
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  2. #2
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    Quote Originally Posted by ewkimchi View Post
    Match each of the following with the correct statement.
    A. The series is absolutely convergent.
    C. The series converges, but is not absolutely convergent.
    D. The series diverges.

    1.
    2.
    3.
    4.
    5.
    The ratio test works well to show if the series are absolutely convergent...

    If \lim_{n \to \infty}\left|\frac{t_{n + 1}}{t_n}\right| < 1 then the series is absolutely convergent, if \lim_{n \to \infty}\left|\frac{t_{n + 1}}{t_n}\right| > 1 the series is divergent, and if \lim_{n \to \infty}\left|\frac{t_{n + 1}}{t_n}\right| = 1, the test is inconclusive and you'll need to use a different test.
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