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Math Help - Series test for absolute/conditional convergence or divergence

  1. #1
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    Series test for absolute/conditional convergence or divergence

    I've been stuck solving two questions:

    1) (-1)^n all over(1 + 1/n)^n^2

    I absolute valued the whole series to get rid of the (-1^n) and got stuck with something that seems almost like e on the bottom. But after applying the ratio test and a poor attempt to convert it into e, I got stuck.


    2) (-1)^n * sin (1/n) all over ((ln(1+n))^2)

    I'm not too sure on how to approach the problem. If I absolute value it and let the limit n tend to infinity, I get 0 over infinity.


    Thank you for the help!
    Last edited by Mondy; September 15th 2010 at 06:12 PM.
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  2. #2
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    Hello,

    For #1:
    The absolute value of it is:

    \sum \dfrac{1}{\left( 1+\frac{1}{n} \right)^{n^2}}=\sum \left( \dfrac{1}{\left( 1+\frac{1}{n} \right)^{n}}\right)^n

    Try the Root Test.


    For #2:
    Try to use the comparison tests for it.
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  3. #3
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    Sweet now I get the first question. Initially I did the same thing and thought that raising it to the n power would only result in n+1 for some odd reason.

    But as for the second series, I used the comparison tests of two separate p series: 1/n and 1/n^2 and neither work. Mind hinting a bit more?
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