Given an=an−1+an−2a_n = a_{n-1} + a_{n-2}an=an−1+an−2 with a0=0,a1=1a_0 = 0, a_1 = 1a0=0,a1=1, what is the Binet's formula for the nnn-th term?
an=ϕn−ψn5a_n = \frac{\phi^n - \psi^n}{\sqrt{5}}an=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
an=ϕn+ψn5a_n = \frac{\phi^n + \psi^n}{\sqrt{5}}an=5ϕn+ψn
an=ϕn−ψna_n = \phi^n - \psi^nan=ϕn−ψn
an=(ϕψ)na_n = (\frac{\phi}{\psi})^nan=(ψϕ)n