why the sequence $ \{q_n \} $ converges to $ + \infty $?

Question

Let $ \alpha \notin \mathbb {Q} $. We know that (according to Liouiville's approximation) for any strictly positive integer $ n $, there exists a strictly positive integer $ p_n $ and an integer $ q_n $ such that $$ | \alpha - \frac{p_n}{q_n} | <\frac {1} {q_n^2} $$ My problem is why the sequence $ \{q_n \} $ converges to $ + \infty $?