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Absolute Value of Limits Proof

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that if bn→b, then the sequence of absolute values |bn| converges to |b|.

    2. Relevant equations



    3. The attempt at a solution

    I've been proving various properties of limits, including product of limits and sum of products, but have been having trouble making progress with the approach to absolute value of limits. I was also wondering is the converse of this is true, that is if |bn|→|b|, is it also true that (bn)→b
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 12, 2012 #2
    Not at all, for example |(-1)^n| -> 1, but (-1)^n doesn't converge at all!
    How about you start by writing down formally the assumption and what you want to prove. You will see that it's pretty straight forward then.
     
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