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Thread: Alternating series

  1. #1
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    Alternating series

    Hi everyone,

    how do i find if the series converges absolutely or conditionally.
    i need help with these question.


    Test the alternating series for convergence or divergence.
    i) \sum^\infty _{n=1} \frac {(-1)^{(n-1)}}{n^\frac {1}{2}}

    my working, by expanding,
    1>0.7071>0.577

    The series converges.
    * i need to find the limit to confirm, how do i do this? is it
    limit \frac {1}{n^\frac{1}{2}} = 0


    thank you for all your help.
    Last edited by anderson; Feb 5th 2010 at 05:22 AM.
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  2. #2
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    By Leibniz test, the series converges.

    Now, in order to study its conditional or absolute convergence, recall the following: if \sum a_n<\infty but \sum|a_n|=\infty, then the series converges conditionally. If \sum a_n<\infty and \sum|a_n|<\infty, then the series converges absolutely.
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  3. #3
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    thank you for helping to clarify, but i need to prove it in the equation, need someone to guide me.

    thank you for help & guidance, really need more help on this...
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  4. #4
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    i gave you the tools to do so!

    show your progress.
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