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Math Help - Series => Convergent or Divergent? (I get 2/5 wrong)

  1. #1
    s3a
    s3a is offline
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    Series => Convergent or Divergent? (I get 2/5 wrong)

    "Match each of the following with the correct statement.
    C stands for Convergent, D stands for Divergent.

    1.
    2.
    3.
    4.
    5. "

    The above is what I did. But according to my school's computer system; 1 and 5 are wrong ... how/why?

    My logic for #1:
    The denominator gets super large so it's like adding 0s in the end so it should converge at some point.

    My logic for #2:
    The denominator again gets larger than the numerator and should eventually be adding 0s.

    What's wrong with my logic?

    Any input would be greatly appreciated!
    Thanks in advance!

    P.S.
    MY answers are:
    1. C (wrong)
    2. C
    3. D
    4. C
    5. C (wrong)
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  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
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    722
    Do you know that

    \sum_{n=1}^{\infty} \frac{1}{n} diverges?


    EDIT: Ill elaborate a bit. You can compare that with the second one you got wrong to see why it will diverge.

    For the first one use the integral test...

    If \int_2^{\infty} \frac{8}{3n\ln(n)} dn < \infty then the series converges, if not then it diverges. (Note the function you integrate must be monotonically decreasing)

    \int_2^{\infty} \frac{8}{3n\ln(n)} dn = \bigg{[}\frac{8}{3}\ln(\ln(n))\bigg{]}_{n=2}^{\infty}.
    Last edited by Deadstar; April 13th 2010 at 02:36 PM.
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