Question

Find an explicit formula for the Fibonacci numbers.

Answer 1

The explicit form of Fibonacci numbers is given by the Binet formula

$F_n=\frac{(1+\sqrt5)^{n+1}-(1-\sqrt5)^{n+1}}{2^{n+1}\sqrt5}, n\geq0$ (see the book Alfred Renyi, Dialogues of math., math collection Trilogy, Publishing House Mir, Moscow, 1980, p.311).