1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Limits question

  1. Feb 7, 2010 #1
    Hello,
    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook