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Math Help - Interval of convergence

  1. #1
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    Interval of convergence

    Find the interval of convergence for the following power series:


    I used the ratio test first to get my radius of convergence which I got to be 6 but I think this is where I may have messed up. From there I added 6 to and subtracted 6 from 2, which would make my interval (-4,8) but its not right so can anyone help?
    Thanks
    AC
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  2. #2
    Ted
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    Post your work to see whats wrong with it.
    PS: the Root Test is better for this one.

    and remember that: \lim_{n\to\infty} n^{\frac{1}{n}} = 1.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    ...

    Solution with test root:

    lim_{n\to\infty} \sqrt[n]{\frac{|(x+2)^n|{6^n}}{7n^4}} = lim_{n\to\infty} \frac{6|(x+2)|}{ \sqrt[n]{7n^4}}=\frac{6|x+2|}{lim_{n\to\infty}\sqrt[n]{7n^4}}=\frac{6|(x+2)|}{1}<1


    So, the interval of convergence is:

    \frac{-1}{6}<x+2<\frac{1}{6}
    \frac{-13}{6}<x<\frac{-11}{6}

    NOW CHECK CONVERGENCE FOR EDGE POINTS:
    Last edited by Also sprach Zarathustra; June 25th 2010 at 05:35 AM. Reason: I was wrong! Thank you Ted.
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  4. #4
    Ted
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    ^^^
    Your solution is wrong.
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