Analyze the convergence or divergence of $\{1/n^2\}$
$\left|\frac{1}{m^2} - \frac{1}{n^2}\right| < \left|\frac{1}{m^2}\right| < \frac{1}{N^2} < \varepsilon$ whenever $N > \dfrac{1}{\sqrt{\varepsilon}}$ (first step because $n^2 > 0$ and hence $\dfrac{1}{n^2} > 0$ and $\dfrac{1}{m^2} - \dfrac{1}{n^2} < \dfrac{1}{m^2}$)
So the sequence is Cauchy and it certainly converges to zero.
Is my approach correct?