A golden number

Suppose that you have a sequence of the type $$\{F_k\}_{k \geq 0},$$ that obeys the rule :

$F_n = F_{n-1}+F_{n-2} \quad \forall n \geq 2.$

Suppose that $$F_0 , F_1 \in \mathbb R_0^{+}$$ are given. Let $$\phi_n = \frac{F_n}{F_{n-1}}$$, $$\ \ \ n >0$$.
What is

$\phi = \lim_{n \rightarrow \infty} \phi_n?$

Rounded your answer to the nearest thousandths.

NOTE : In regards to some complains I have had, I would like to stress that : $$\forall n>0, \ \phi_n >0$$.

×

Problem Loading...

Note Loading...

Set Loading...