Limit Question involving Fibonacci Sequence.

[mmmboh]

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

I believe I know what technique I have to use. I think I have to find two subsequences of (x_n), 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

 

[vela]

Does it help to use the fact that f_n+1=f_n+f_n-1?

 

[mmmboh]

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.

 

[vela]

Well, what's f_n-1/f_n in terms of the x sequence?