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Analysis Applying Combination Rules

  1. Jan 7, 2010 #1
    True or False, with a proof or counterexample.

    a) If bn ≠ 0 and an/bn →1, then an-bn → 0
    b) If bn ≠ 0, bn is bounded and an/bn → 1 then an-bn → 0

    At the moment I cannot even see which is false so I am struggling with this question. I think the proof will require use of the quotient combination rule and the sum combination rule but I cannot see where to start! Any help would be appreciated!
  2. jcsd
  3. Jan 7, 2010 #2
    Do you at least have a guess?
  4. Jan 7, 2010 #3
    Yes! Sorry I am new so wasnt sure how this all worked!

    Basically I think the first is false and the second true!
    I think this because for the second one,
    if i use the fact that an/bn →1
    I can say that
    |an-bn| = bn |an/bn -1| → 0 because bn is bounded.

    I think this works?

    I can't really prove that the first is false, but I am working on that one at the moment! Any help would be great!
  5. Jan 7, 2010 #4
    Yes. That absolutely works for the second. For the first consider a_n = n + 1 and b_n = n.
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