Results 1 to 5 of 5

Math Help - [SOLVED] Contracting but not converging ?

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    9

    [SOLVED] Contracting but not converging ?

    Title says it all. I have to find a non converging sequence such that:

    \left| t_{n+1} - t_{n} \right| < \left| t_{n} - t_{n-1} \right| \forall n \geq 2

    I just can't seem to find any such sequence and it seems to me that the definition implies that any such sequence must be converging. Any hint/thought would be appreciated!

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Let t_n= \sum_{j=1} ^{n} \ \frac{1}{j}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    Posts
    9
    Why wouldnt such a sequence be converging?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,403
    Thanks
    1486
    Awards
    1
    Quote Originally Posted by Jose27 View Post
    Let t_n= \sum_{j=1} ^{n} \ \frac{1}{j}
    Quote Originally Posted by tyro89 View Post
    Why wouldnt such a sequence be converging?
    Have you heard of the harmonic series?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2008
    Posts
    9
    I have now thank's a lot ! Based on what have been thaught up to now in my class this was really an odd question...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Converging Subsequence
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: August 20th 2011, 08:53 AM
  2. Strictly contracting sequences
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 23rd 2008, 06:36 AM
  3. Converging integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 12th 2008, 05:37 PM
  4. [SOLVED] subsequences converging
    Posted in the Calculus Forum
    Replies: 6
    Last Post: November 21st 2007, 08:28 AM
  5. converging with e
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 11th 2007, 11:00 PM

Search Tags


/mathhelpforum @mathhelpforum