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Math Help - Radii of Convergence

  1. #1
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    Radii of Convergence

    The problem says to find the radii of convergence of these two functions:

    2-\sqrt{1+x^2}

    1-\ln{(1+x^2)}

    But I am not sure how to do this. Could you just take the limit of each and set that to be less than 1? I am just not sure how to approach this problem. Thanks ahead of time for the help.
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  2. #2
    Member Miss's Avatar
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    Quote Originally Posted by Spudwad View Post
    The problem says to find the radii of convergence of these two functions:

    2-\sqrt{1+x^2}

    1-\ln{(1+x^2)}

    But I am not sure how to do this. Could you just take the limit of each and set that to be less than 1? I am just not sure how to approach this problem. Thanks ahead of time for the help.
    "Raduis of convergence" for the infinite series only ..
    I do not see any series here ..
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  3. #3
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    Quote Originally Posted by Miss View Post
    "Raduis of convergence" for the infinite series only ..
    I do not see any series here ..
    That's partly why I am stuck and if that is the case, then I will make sure to bring it up with my instructor.
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  4. #4
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    Quote Originally Posted by Spudwad View Post
    The problem says to find the radii of convergence of these two functions:

    2-\sqrt{1+x^2}

    1-\ln{(1+x^2)}

    But I am not sure how to do this. Could you just take the limit of each and set that to be less than 1? I am just not sure how to approach this problem. Thanks ahead of time for the help.

    You may write these as infinite series...

    2-\sqrt{1+x^2}=2-\left(1+x^2\right)^{\frac{1}{2}}

    This may be expanded as a series, as can the natural log.
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