Results 1 to 5 of 5

Math Help - help! show this sequence is Cauchy

  1. #1
    Junior Member mremwo's Avatar
    Joined
    Oct 2010
    From
    Tampa, FL
    Posts
    53

    help! show this sequence is Cauchy

    Suppose that 0<r<1 and  \ \mid x_{n+1} - x_{n} \mid \ < r^n \ \forall n \in N
    Show that (x_{n}) is Cauchy.

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by mremwo View Post
    Suppose that 0<r<1 and  \ \mid x_{n+1} - x_{n}\mid \ \forall n \in N Show that (x_{n}) is Cauchy.
    There is a great deal missing here.
    In fact, there is no question there what so ever.
    Please edit your post.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member mremwo's Avatar
    Joined
    Oct 2010
    From
    Tampa, FL
    Posts
    53
    yes i just edited it! sorry!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    Some hints:

    Use the generalized triangle inequality.

    \sum r^n is a convergent geometric series, thus the "tail" of the series can be made arbitrarily small.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member mremwo's Avatar
    Joined
    Oct 2010
    From
    Tampa, FL
    Posts
    53
    I'm sorry, I still have no idea what to do. Could you give me another hint? This concept is very hard for me to grasp


    EDIT: nevermind, i got it! thank you!
    Last edited by mremwo; February 16th 2011 at 09:30 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Subsequence of a Cauchy Sequence is Cauchy
    Posted in the Differential Geometry Forum
    Replies: 9
    Last Post: September 30th 2010, 01:29 AM
  2. cauchy sequence, contractive sequence
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 25th 2010, 06:25 AM
  3. Cauchy Sequence
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 16th 2010, 06:10 PM
  4. cauchy sequence
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: December 28th 2009, 08:37 AM
  5. Cauchy sequence
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 23rd 2009, 03:30 AM

Search Tags


/mathhelpforum @mathhelpforum