Finding N for Fibonacci ratios converging to golden ratio

[leoflc]

Fibonaci Sequence,
{1,1,2,3,4,8,13}
If you take successive ratios of these term, we generate a realted sequence,
{1/1, 1/2, 2/3, 3/5, 5/8, 8/13}
and this sequence converges to the Golden Mean. Using the formal definition of convergence, find the appropriate $N$ if $\varepsilon = 0.0001$
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I know Fibonnaci Sequence is $a_n = a_{n-1} + a_{n+1}$
and I need to find the limit for the Golden Mean?

could anyone give me a hand?
Thank you very much!

 

[photon_mass]

what is the formula of the related sequnce?
this is the sequence you are concerned with.

 

[leoflc]

I'm still working on the formula for the Golden Mean, but is it $$\frac{(n-1)+(n-2)}{n+1}$$
?

 

[Tide]

Hint:

$$\frac {a_{n+1}}{a_n} = 1 + \frac {a_{n-1}}{a_n}$$