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Convergence Induction

  1. Feb 9, 2012 #1
    1. The problem statement, all variables and given/known data
    If (an) — > 0 and \bn - b\ < an, then show that (bn) — > b


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 9, 2012 #2
    Please show your attempt at the solution.
     
  4. Feb 9, 2012 #3
    Since an --> 0, given some epsilon>0, there exists and m>0 such that /an-0/=/an/<epsilon for all n>m
    thus, /bn-b/</an/<epsilon for all n>m
    therefore, by definition bn-->b
     
  5. Feb 9, 2012 #4

    Dick

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    Looks ok to me.
     
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