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Component of Fibonacci Sequence

  1. Oct 18, 2006 #1
    Please excuse my total ignorance but can someon explain to me how the following part of a certain proof makes sense

    We want to show that Fk+1 ≤ (7/4)^(k+1). Consider fk+1 = fk + fk−1 (We can do this
    as k +1 is at least 2; see the comment following the basis) < (7/4)^k +(7 /4)^(k−1) (by the Induction Hypothesis;
    notice how the stronger hypothesis comes in handy here.)

    The parts I bolded in red are mainly the things I dont understand. I plugged in the (7/4)...part into my calculator and did not get the alleged answer I was supposed to get if it were simply (7/4)^k+1. Can someone please enlighten me? :bugeye:
  2. jcsd
  3. Oct 18, 2006 #2

    matt grime

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    If a<b, and c>0, then ac<bc (and no that is not cryptic - you end up with something that you wish to show is less than something else - there is no reason to suppose they are equal, nor is it necessary. If I want to show something is less than 4 and I show it is less than 3 I've shown it is less than 4, for example).
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