Show that $\sum_{n=2}^\infty \frac{1}{[n+(-1)^n]^2}$ converges.

Show that $\sum_{n=2}^\infty \frac{1}{[n+(-1)^n]^2}$ converges.

How do I show that this series $\sum_{n=2}^\infty \frac{1}{[n+(-1)^n]^2}$
converges??