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Math Help - Maclaurin Series

  1. #1
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    Maclaurin Series

    How can I find the Maclaurin series for (z/z^3 + 8) and find the radiance of convergence?
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by ihr02 View Post
    How can I find the Maclaurin series for (z/z^3 + 8) and find the radiance of convergence?
    One way to do it is this:

    \frac{z}{z^3+8}=\frac{z}{8}\cdot\frac{1}{1+\left(\  frac{z}{2}\right)^3}
    Now you can substitute \left(\frac{z}{2}\right)^3 for u in \frac{1}{1+u}=\sum_{k=0}^\infty(-1)^k u^k to get

    =\frac{z}{8}\cdot\sum_{k=0}^\infty (-1)^k\left(\frac{z}{2}\right)^{3k} = \sum_{k=0}^\infty \frac{(-1)^k}{2^{3(k+1)}}z^{3(k+1)}.
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