Limit Question involving Fibonacci Sequence.

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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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