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Math Help - Radius of Convergence

  1. #1
    Member iPod's Avatar
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    Radius of Convergence

    Hello,
    I have to find the radius of convergence with this series

    \Sigma 2^{-n}z^{n^2}}

    I've tried the root test and the ratio test but the solution they give seem inconclusive, is the any clues as to what I should do?
    Thank you
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  2. #2
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    Re: Radius of Convergence

    Quote Originally Posted by iPod View Post
    Hello,
    I have to find the radius of convergence with this series

    \Sigma 2^{-n}z^{n^2}}

    I've tried the root test
    The root test works. For what values does {\lim _{n \to \infty }}\frac{{{z^n}}}{2} converge?
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  3. #3
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    Re: Radius of Convergence

    Oh I see, so basically it converges to 0 if |z|<1, meaning the series converges anywhere (provided |z|<1)
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  4. #4
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    Re: Radius of Convergence

    Actually, |z|<2 because it's |z/2| < 1
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  5. #5
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    Re: Radius of Convergence

    Quote Originally Posted by iPod View Post
    Actually, |z|<2 because it's |z/2| < 1
    NO! you were right the first time.

    Look at the webpage.

    You can play around with the numerator to see how it works.
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