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Homework Help: Limits question

  1. Feb 7, 2010 #1
    I'm having trouble with this question.
    Let Sn be a sequence that converges. Show that if Sn <= b for all but finitely many n, then lim sn <= b.
    This is what I'm trying to do, assume s = lim Sn and s > b. (Proof by contradiction) abs(Sn-s) < E, E > 0. Don't know what to do from there, but maybe set E = s -b. E is epsilon by the way. Probably to start using latex...

    If any one could help, that would be awesome.
  2. jcsd
  3. Feb 7, 2010 #2
    Your idea is fine so far. Now what does [tex]|s_n - s| < \epsilon = s-b[/tex] for all n > N imply?
  4. Feb 7, 2010 #3
    s is a upper bound, so the Sn-s is negative. So abs(Sn-s) < s -b doesn't hold true all n. I'm not sure though
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