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Math Help - what is the radius of convergence of that power series

  1. #1
    Junior Member sorv1986's Avatar
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    Talking what is the radius of convergence of that power series

    how to determine the radius of convergence of the power series

    Σ 2^(n) z^(nē).



    thanks in advance .regards.
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    MHF Contributor Drexel28's Avatar
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    Re: what is the radius of convergence of that power series

    Quote Originally Posted by sorv1986 View Post
    how to determine the radius of convergence of the power series

    Σ 2^(n) z^(nē).



    thanks in advance .regards.
    I think if you try the root test you'll quickly see that the answer is 1.
    Last edited by Drexel28; December 2nd 2011 at 09:30 AM.
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    Opalg's Avatar
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    Re: what is the radius of convergence of that power series

    Quote Originally Posted by sorv1986 View Post
    how to determine the radius of convergence of the power series

     \sum 2^n z^{nē}.
    Treat it as an ordinary series (rather than a power series) and use the ratio test:

     \frac{(n+1)\text{th term}}{n\text{th term}} = \frac{2^{n+1}z^{(n+1)^2}}{2^nz^{n^2}} = 2z^{2n+1}.

    The limit of that as n\to\infty will depend on whether or not |z|<1.
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