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Convergent non-monotone sequences

  1. Apr 30, 2009 #1
    1. The problem statement, all variables and given/known data

    Let C=[tex]\bigcup[/tex]n=1[tex]\infty[/tex]Cn where Cn=[1/n,3-(1/n)]
    a) Find C in its simplest form.
    b)Give a non-monotone sequence in C converging to 0.

    2. Relevant equations


    3. The attempt at a solution
    For part a) i get C=[0,3]. Is this correct? im not sure as to wether 0 and 3 are contained in the set though. Should it be C=(0, 3)?

    As for part b) im not really sure here. I thought one such sequence might be
    (1, 2, 1/2, 1/3, 1/4, 1/5,...). So the tail converges to zero and the first 2 terms mean it is non-monotone.
    [
     
  2. jcsd
  3. Apr 30, 2009 #2

    tiny-tim

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    Hi Easty! :smile:
    Well, by definition of union, 0 is only in C if it's in one of the Cns … is it? :wink:
    hmm … seems a daft question :rolleyes:

    but I suspect they want it to be non-monotone wherever you start.
     
  4. Apr 30, 2009 #3
    Ok then so it must be C=(0, 3).

    As for part b would this sequence work:
    (1/n*sin(n)).
    It should converge by the absolute convergence theorem i think.
    I'd appreciate any comments or criticisms.
    thanks
     
  5. May 1, 2009 #4

    tiny-tim

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    Yup! :biggrin:
    Yes, almost any daft sequence works! :smile:
     
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