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Math Help - Manipulating power series

  1. #1
    Senior Member mollymcf2009's Avatar
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    Manipulating power series

    Find a power series representation of the function:

    f(x) = \frac{8}{1-x^7}

    and determine the interval of convergence.

    Here is my work:

    8 \sum^{\infty}_{n=0} (x^7)^n

     = \sum^{\infty}_{n=0} 8x^{7n}

    Ok, I found my interval of convergence:

    -1 < x <1

    But to test each end point, where do I plug those into? Into the series (x^7)^n ?
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  2. #2
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    the end points are x=1 and x=-1, so you must change x by those values in the series and determine its convergence
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