There are many different tests to tell if a series converges or diverges. The integral test is one way to do so. As long as 1) The series is decreasing as it approaches infinity, and 2) The series remains positive, you can perform the integral test. Once those two conditions are met, perform as if the series is just an improper integral, and evaluate it and see if it converges or diverges (refer to this page for help with improper integrals).
Steps: 1. Check if terms of the series decrease as the series approaches infinity 2. Check if terms of the series remain positive as the series approaches infinity 3. If both steps 1 and 2 check out, treat the series as an improper integral, and evaluate