Results 1 to 6 of 6

Math Help - Obtaining a sequence in a set converging to supS and infS

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    40

    Obtaining a sequence in a set converging to supS and infS



    Any help please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Feb 2009
    Posts
    40
    I've figured out A.. I just need help with B.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Mar 2009
    Posts
    256
    Thanks
    1
    Quote Originally Posted by qtpipi View Post


    Any help please?
    if my intuition is correct without any solid proof the sequences in concern are:

    \frac{2+(-1)^n}{n} and \frac{2+(-1)^n}{n}+1

    or the sequences \frac{3}{2k}+1 and \frac{1}{2k+1} which are the two subsequences of the major sequence
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1
    S = \left\{ {\frac{{2 + \left( { - 1} \right)^n }}<br />
{n}:n \in \mathbb{Z}^ +  } \right\},~\inf (S) = 0,~\sup (S) = \frac{3}{2}.
    Clearly there are subsequences converging to 0 but none converging to \frac{3}{2}.
    Last edited by Plato; April 27th 2009 at 11:52 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Banned
    Joined
    Mar 2009
    Posts
    256
    Thanks
    1
    But for n=2 s_{2}=\frac{2+1}{2} = \frac{3}{2}\geq 1???

    And s_{2}\in S ???
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1
    Quote Originally Posted by xalk View Post
    But for n=2 s_{2}=\frac{2+1}{2} = \frac{3}{2}\geq 1???
    You are quite right. I corrected the mistake.
    Last edited by Plato; April 27th 2009 at 12:06 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Converging/Diverging Sequence
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 17th 2010, 02:29 PM
  2. Sequence converging to Zero.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 28th 2009, 09:41 AM
  3. converging sequence?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 29th 2009, 02:46 PM
  4. Converging sequence.
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: November 25th 2008, 10:49 AM
  5. Converging Sequence
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 16th 2008, 10:55 AM

Search Tags


/mathhelpforum @mathhelpforum