KURSCHAK 2002 Problem 2

The Fibonacci sequence is defined as $f_1=f_2=1$ , $f_{n+2}=f_{n+1}+f_n$ ( $n\in\mathbb{N}$ ). Suppose that $a$ and $b$ are positive integers such that $\frac ab$ lies between the two fractions $\frac{f_n}{f_{n-1}}$ and $\frac{f_{n+1}}{f_{n}}$ . Show that $b\ge f_{n+1}$ .