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Math Help - Alternating series

  1. #1
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    Alternating series

    summation:

    \sum\limits_{n=0} ^\infty \frac{(-1)^{n+1}n^n}{3^n^2}

    Using the root test and dropping the (-1)^{n+1} I got:

    ^n\sqrt{\frac{n^n}{3^n^2}}

    simplifies to:

    \frac{n}{3^n}

    To me it appears that any positive integer used will give the result of a ratio value of less than 1 and thus converges. However, wolfram tells me that it actually diverges. What am I doing wrong??
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  2. #2
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    Re: Alternating series

    how did you enter it in Wolfram?
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  3. #3
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    Re: Alternating series

    Dangit, I missed a carrot after the 3 in the denominator in wolfram. Now it works. I kept checking it but didn't notice the mistake until you asked that. Thanks a lot for the help
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