Here is the problem:

Define the sequence {$\displaystyle a_n$} by $\displaystyle a_{n+1} = (a_n)^2$ for all $\displaystyle n\in\mathbb{N}$ where $\displaystyle 0<a_1\leq\frac{1}{3}$.

Prove that {$\displaystyle a_n$} is contractive.

Any advice and or solutions? thanks a lot