Results 1 to 2 of 2

Math Help - Sequence of function 2

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Sequence of function 2

    Let (f_n)^\infty_{n=1} a sequence of function which defined recursively on interval  [a,b] :

    f_n(x)=\sqrt{xf_{n-1}(x)}, f_0(x)\equiv1

    1. Prove that the sequence (f_n)^\infty_{n=1} converges on interval  [a,b] to limit continuous function f.

    2. Prove that the convergence is uniform.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2010
    Posts
    12
    See the attachment.
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: October 26th 2010, 10:23 AM
  2. Sequence of function.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: June 5th 2010, 08:36 PM
  3. Sequence of function 3
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: June 5th 2010, 12:51 PM
  4. sequence, analytic function
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 17th 2010, 09:16 AM
  5. Find the function from a sequence.
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: February 8th 2009, 08:20 AM

Search Tags


/mathhelpforum @mathhelpforum