If $\displaystyle a=\frac{1+\sqrt{5}}{2}$ and $\displaystyle b=\frac{1-\sqrt{5}}{2}$, prove that $\displaystyle f\_n=\frac{a^n-b^n}{\sqrt{5}}$ for all $n\in\mathbb{P}$

Would we start with a base case for proof of induction?

In that case, $n=0$ would be the base case

so how would you prove for $n$ and $n+1$?