Leonardo Pisano Fibonacci

1. Fibonacci Sequence

A sequence where each number is the sum of the two preceding ones.

$$ F_n = F_{n-1} + F_{n-2}, \quad F_0=0, F_1=1 $$

2. Golden Ratio limit

The ratio of consecutive Fibonacci numbers converges to \(\phi\).

$$ \lim_{n \to \infty} \frac{F_{n+1}}{F_n} = \phi = \frac{1+\sqrt{5}}{2} $$