Remember that the Fibonnaci Sequence is the sequence described by f(0)=1, f(1)=1, with f(n) = f(n-1) + f(n-2). We are interested in the the ratio f(n+1)/f(n). Let's call the the ratio

We can assume that the limit of xsub n as n approachs infinity is x.

So,

or

Since we are dealing only with positive values of x,

which equals the golden ratio 1.618033988738303.

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