Results 1 to 2 of 2

Math Help - Uniform Convergence Proof

  1. #1
    Member
    Joined
    Mar 2012
    From
    USA
    Posts
    92

    Uniform Convergence Proof

    I'm having trouble getting this proof, uniform convergence has always been a hard thing for me.

    If Σk=0infinity ak converges absolutely, prove that Σk=0infinity akxk converges uniformly on [-1,1]

    Since this is a power series, I thought I'd go the approach that if akxk converges absolutely for x=1, then it converges uniformly for [-1,1]. I'm not sure this is the right approach though, since I'm having trouble starting.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,517
    Thanks
    771

    Re: Uniform Convergence Proof

    It's simple: the remainder \left|\sum_{k=N}^\infty a_kx^k\right| \le \sum_{k=N}^\infty \left|a_kx^k\right| \le \sum_{k=N}^\infty \left|a_k\right| < \varepsilon for a sufficiently large N.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 18
    Last Post: April 12th 2012, 02:34 PM
  2. Pointwise and uniform convergence proof?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 16th 2012, 03:03 AM
  3. Replies: 1
    Last Post: October 31st 2010, 07:09 PM
  4. Replies: 2
    Last Post: April 11th 2010, 02:45 PM
  5. Uniform Continuous and Uniform Convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 28th 2007, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum