MathItems

Let $F_n$ be the Fibonacci numbers. Then

F_n = \frac{\phi^n - \hat{\phi}\strut^n}{\sqrt{5}}

for $n \geq 0$, where $\phi = \tfrac{1}{2}(1 + \sqrt{5})$ and $\hat{\phi} = \tfrac{1}{2}(1 - \sqrt{5})$.