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Math Help - Assistance on a recursive proof

  1. #1
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    Assistance on a recursive proof

    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 sqrt(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.
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  2. #2
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    Re: Assistance on a recursive proof

    Hey kkar.

    As an alternative, have you tried expanding out the sequence using definitions for A_n+k in terms of all the ones less than n+k?
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