Let $\mathbb{Q}_{\geq 1}=\{r\in\mathbb{Q}\,|\,r\geq 1\}$. Once $\mathbb{Q}$ is enumerable, $\mathbb{Q}_{\geq 1}$ is also enumerable. Let $\{r_1,r_2,\ldots\}$ be such an enumeration. What can we say about
$$\sum_{n=1}^{\infty}\frac{1}{r_n^2}$$
does it converge or does it diverge?
It diverges, and the answer doesn't depend on which enumeration you use (since all the terms are positive). Indeed, $$ \sum_{n=1}^\infty \frac1{r_n^2} = \sum_{\substack{r\in\Bbb Q \\ r\ge1}}\frac1{r^2} \ge \sum_{\substack{r\in\Bbb Q \\ 1\le r\le 2}}\frac1{r^2} \ge \sum_{\substack{r\in\Bbb Q \\ 1\le r\le 2}} \frac14, $$ and the last sum is certainly divergent.