How can I check the convergence of

$$\sum\_{k=2}^\infty \frac{1}{k^2-1}$$

? As it's almost the same as

$$\sum\_{k=2}^\infty \frac{1}{k^2}$$

which converges, it should converge, but I can't use a comparison between the two here, as

$$\sum\_{k=2}^\infty \frac{1}{k^2-1} \geq \sum\_{k=2}^\infty \frac{1}{k^2}$$

so it wouldn't help. So how should I go about it?