Binet's formula is an equation which gives the th Fibonacci number as
a difference of positive and negative th powers of the golden ratio . It can be written as

(1)

(2)

Binet's formula is a special case of the Binet form with It was derived by Binet in 1843, although the result was
known to Euler, Daniel Bernoulli, and de Moivre more than a century earlier.