Limit Question involving Fibonacci Sequence.

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Homework Help Overview

The discussion revolves around a limit question involving the Fibonacci sequence, specifically analyzing the ratio of consecutive Fibonacci numbers. The original poster is attempting to determine the limit of the sequence defined by the ratio of consecutive Fibonacci numbers.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster considers using subsequences of the ratio sequence but struggles to find a suitable relationship between them. Another participant suggests leveraging the recursive definition of Fibonacci numbers to aid in the analysis.

Discussion Status

The conversation shows some progression, with the original poster expressing a realization after a suggestion was made. However, further clarification is sought regarding the relationship between the ratios and the Fibonacci sequence.

Contextual Notes

The original poster is preparing for an analysis exam, indicating a time constraint and the need for clarity in understanding the problem. There is an implicit assumption that the limit exists, which is central to the discussion.

mmmboh
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I'm reviewing for my analysis exam, and am having trouble with this question: Let (fn) be the Fibonacci sequence and let xn=fn+1/fn. Given that lim (xn) = L exists, find L.

I believe I know what technique I have to use. I think I have to find two subsequences of (xn), write one in terms of the other, equate them, and since they have the same limit solve for L, but I can't find a subsequence that I can write in terms of the other, I have tried even n, odd n, n2, etc.

Can someone help?

Thanks
 
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Does it help to use the fact that fn+1=fn+fn-1?
 
Ugh I see. Wow that was easy...and I actually did try using that, for some reason you writing it made me see the answer. Thanks.
 
Well, what's fn-1/fn in terms of the x sequence?
 

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