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Assistance on a recursive proof

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Define a sequence of numbers Ai by: A0 = 2, An+1 = An/2 + 1/An (for n greater than or equal to 1). Prove that An less than or equal to √(2) + 1/2n for all n greater than or equal to 0. I think it's a safe bet that induction should be used here. I'm having trouble finding the inductive step though maybe just cause I'm not feeling particularly well today. Help is always appreciated.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 28, 2012 #2

    tiny-tim

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    hi black_hole! :smile:
    yes …

    just put it into the equation! :rolleyes:
     
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