Which of the following is true regarding the Fibonacci sequence Fn=Fn−1+Fn−2F_n = F_{n-1} + F_{n-2}Fn=Fn−1+Fn−2 with F0=0,F1=1F_0=0, F_1=1F0=0,F1=1?
Fn=ϕn−ψn5F_n = \frac{\phi^n - \psi^n}{\sqrt{5}}Fn=5ϕn−ψn where ϕ=1+52,ψ=1−52\phi = \frac{1+\sqrt{5}}{2}, \psi = \frac{1-\sqrt{5}}{2}ϕ=21+5,ψ=21−5
Fn=ϕn+ψn5F_n = \frac{\phi^n + \psi^n}{\sqrt{5}}Fn=5ϕn+ψn
Fn=ϕn+ψnF_n = \phi^n + \psi^nFn=ϕn+ψn
Fn=ϕn−ψn2F_n = \frac{\phi^n - \psi^n}{2}Fn=2ϕn−ψn