Results 1 to 4 of 4

Thread: Radii of Convergence

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    36

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Miss's Avatar
    Joined
    Mar 2010
    From
    Planet earth.
    Posts
    165
    Thanks
    1
    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 ..
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    36
    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.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Define the relationship of two radii
    Posted in the Geometry Forum
    Replies: 3
    Last Post: March 17th 2010, 08:04 AM
  2. radii of convergence question
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: January 7th 2010, 01:04 PM
  3. Radii of convergence
    Posted in the Calculus Forum
    Replies: 16
    Last Post: November 23rd 2008, 09:49 AM
  4. two radii with a common tangent
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 21st 2006, 11:36 AM
  5. Radii of convergence of a power series
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 11th 2006, 02:21 PM

Search Tags


/mathhelpforum @mathhelpforum