Proving a sequence is Null, Help!

Question

I have this question: Use the definition of a null sequence to prove that the sequence $\{a_n\}$ given by $a_n = \dfrac{2}{2n^2 -3}, n = 1, 2, \dots ,$ is null. So I know that we want to show for $\epsilon >0 $there is an integer $N$ that $\dfrac{2}{2n^2 -3}<\epsilon.$ But how do I do this?

Answer 1

Hint: $2n^2 - 3 > n^2 > n, \forall n \geq 2 \Rightarrow \dfrac{2}{2n^2-3} < \dfrac{2}{n}, \forall n \geq 2.$