## Closed-form expression

Like every sequence defined by linear recurrence,

^{[16]}the Fibonacci numbers have a closed-form solution. It has become very well known asBinet‘s formula, even though it was already known by Abraham de Moivre:^{[17]}

where

is the golden ratio (sequence A001622 in OEIS).

That

follows from the defining equation above.

The Fibonacci recursion

is similar to the defining equation of the golden ratio in the form

which is also known as the generating polynomial of the recursion.

via en.wikipedia.org