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Math Help - Limit of ratio of Non-consecutive terms of Fibonacci Sequence

  1. #1
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    Limit of ratio of Non-consecutive terms of Fibonacci Sequence

    Hi folks,
    If anyone can help with this 'd be delighted. I can prove that the limit of the ratio of consecutive terms of the FS is PHI. However, how do I go about proving that the limit of NON-consecutive terms is phi to the power of t eg
    Lim n--->inf (Un/Un+t)=Phi^t
    Any help would be appreciated,
    Thanks
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  2. #2
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    Re: Limit of ratio of Non-consecutive terms of Fibonacci Sequence

    Hi,
    I've attached a proof.

    Limit of ratio of Non-consecutive terms of Fibonacci Sequence-mhffibonacci.png
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