<s>[INST] The recursive formula for Fibonacci numbers is as follows: $F(1)=1$, $F(2)=1$, $F(n)=F(n-1)+F(n-2)$ for $n \ge 3$. The explicit formula for Fibonacci numbers is as follows: $F(n)=\frac{1}{\sqrt{5}}[\phi^n-(1-\phi)^n]$, where $\phi$ is the golden ratio such that $\phi^2 = \phi + 1$. Prove that the recursive formula for Fibonacci numbers implies the explicit formula for Fibonacci numbers.[/INST]