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Math Help - Divergence of a series

  1. #1
    Junior Member
    Joined
    Dec 2008
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    70

    Divergence of a series

    Face with the series;

    Sum from n=1 to infinity of: n/(1+n),

    And i'm asked to use any relevant tests and then determine if it converges or not.

    I used the ratio test and got it to =1 therefore inconclusive, root test doesnt seem applicable, can't use integral test as the function is not decreasing, is all that correct and is what i've done below correct,

    lim (as n --> inf) (n/(1+n)) is 1 as co-efficients of two greatest growing terms are 1/1, as limit doesn't equal 0 the series is divergent.

    I'm really unsure with this stuff applying the tests seems simple but the text i have is very shady on how to otherwise deal with the series.

    Any help would be GREATLY appreciated.

    Cheers.
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  2. #2
    Senior Member
    Joined
    Feb 2010
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    Yes, that is correct. The terms must go to zero in order for a series to converge. You should try this test first when faced with a series.
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