Results 1 to 4 of 4

Math Help - question regarding contractive sequence

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    104

    question regarding contractive sequence

    Here is the problem:
    Define the sequence { a_n} by a_{n+1} = (a_n)^2 for all n\in\mathbb{N} where 0<a_1\leq\frac{1}{3}.
    Prove that { a_n} is contractive.
    Any advice and or solutions? thanks a lot
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by dannyboycurtis View Post
    Here is the problem:
    Define the sequence { a_n} by a_{n+1} = (a_n)^2 for all n\in\mathbb{N} where 0<a_1\leq\frac{1}{3}.
    Prove that { a_n} is contractive.
    Any advice and or solutions? thanks a lot

    What is a "contractive sequence", anyway?

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1
    Quote Originally Posted by tonio View Post
    What is a "contractive sequence", anyway?
    I have wondered the same thing?
    I know about Contraction mapping in a metric space.
    Here is the only fact that I can relate it to: 0 < a < 1\, \Rightarrow \,a^2  < a.
    Last edited by Plato; October 9th 2009 at 03:02 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. cauchy sequence, contractive sequence
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 25th 2010, 06:25 AM
  2. Contractive Map
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 18th 2008, 11:20 AM
  3. contractive sequence
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 11th 2008, 09:40 AM
  4. Proof of contractive sequence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2007, 07:50 AM
  5. Contractive Sequence
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 25th 2006, 10:04 AM

Search Tags


/mathhelpforum @mathhelpforum