This is the question 4(h), 3.1.5, Mathematical Analysis I by Zorich.
In part (g), I was given that $$ \frac{1+\sqrt{5}}{2}=1+\frac{1}{1+\frac{1}{1+\ldots}}, $$ and I think I should use this to prove the Binet's formula $$ u_{n}=\frac{1}{\sqrt{5}}\left[\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}\right]. $$
How can I solve it? It is okay to just give a hint so that I can work out myself.