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Math Help - converge and diverge problem

  1. #1
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    converge and diverge problem

    Does this problem converge absolutely, conditionally, or does it diverge?

    the equation: [url=http://img219.imageshack.us/img219/5968/untitled7gf.jpg[/url]

    also, the hint is to first show that ln(1 + x) <= x if x > 0

    Thanks for any help.
    Attached Thumbnails Attached Thumbnails converge and diverge problem-gash.jpg  
    Last edited by CaptainBlack; January 24th 2007 at 08:19 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rcmango View Post
    Does this problem converge absolutely, conditionally, or does it diverge?

    the equation: [url=http://img219.imageshack.us/img219/5968/untitled7gf.jpg[/url]

    also, the hint is to first show that ln(1 + x) <= x if x > 0

    Thanks for any help.
    As the term inside the log is monotonicaly decreasing and goes to 1 as n
    goes to infinity, the log term is monotonicaly decreasing and goes to zero,
    thus by the alternating series test the series converges. See the other
    for details or this link.

    The hint tells us that ln(1+1/n^2)<1/n^2, and as sum(1/n^2, n=1,..., infty)
    does converge the series is also absolutly convergent.

    RonL
    Last edited by CaptainBlack; January 24th 2007 at 10:08 AM.
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