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Homework Help: Help, about Fibonnaci Sequence / Golden Mean

  1. Sep 29, 2004 #1
    Fibonaci Sequence,
    {1,1,2,3,4,8,13}
    If you take successive ratios of these term, we generate a realted sequence,
    {1/1, 1/2, 2/3, 3/5, 5/8, 8/13}
    and this sequence converges to the Golden Mean. Using the formal definition of convergence, find the appropriate [itex] N [/itex] if [itex] \varepsilon = 0.0001[/itex]
    ------------------------------------------------------------------
    I know Fibonnaci Sequence is [itex] a_n = a_{n-1} + a_{n+1} [/itex]
    and I need to find the limit for the Golden Mean?

    could anyone give me a hand?
    Thank you very much!
     
    Last edited: Sep 29, 2004
  2. jcsd
  3. Sep 29, 2004 #2
    what is the formula of the related sequnce?
    this is the sequence you are concerned with.
     
  4. Sep 29, 2004 #3
    I'm still working on the formula for the Golden Mean, but is it [tex]\frac{(n-1)+(n-2)}{n+1}[/tex]
    ?
     
  5. Sep 29, 2004 #4

    Tide

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    Hint:

    [tex]\frac {a_{n+1}}{a_n} = 1 + \frac {a_{n-1}}{a_n}[/tex]
     
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