For the series, determine if it's okay to use the integral test. If so, use the integral test to determine whether the series converges or diverges.
is non-negative and decreasing. Integrating this requires a formula:
The arctan function approaches as x goes to infinity:
This means the integral works out to
We don't know what this number is, but it's a finite number, and that's all that matters. The improper integral converges, and by the integral test the series does too.