Results 1 to 2 of 2

Math Help - Proof of contractive sequence

  1. #1
    Newbie
    Joined
    Mar 2007
    Posts
    21

    Proof of contractive sequence

    A sequence (Sn) is said to be contractive if there exists k with 0<k<1 such that |S(n+2) - S(n+1)| <= k|S(n+1) - Sn| for all n is an element of N. Prove that every contractive sequence is a Cauchy sequence, and hence is convergent
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by learn18 View Post
    A sequence (Sn) is said to be contractive if there exists k with 0<k<1 such that |S(n+2) - S(n+1)| <= k|S(n+1) - Sn| for all n is an element of N. Prove that every contractive sequence is a Cauchy sequence, and hence is convergent
    I did not see the problem. But do not accuse other people on this forum by not helping you . Yes, this is a harder problem. I am not going to write out the full proof, the general idea is contained in the image below.
    Attached Thumbnails Attached Thumbnails Proof of contractive sequence-picture6.gif  
    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, 07:25 AM
  2. question regarding contractive sequence
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: October 9th 2009, 05:36 PM
  3. Contractive Map
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 18th 2008, 12:20 PM
  4. contractive sequence
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 11th 2008, 10:40 AM
  5. Contractive Sequence
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 25th 2006, 11:04 AM

Search Tags


/mathhelpforum @mathhelpforum