# A golden number

**Discrete Mathematics**Level 4

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 : \( \forall n>0, \ \phi_n >0 \).