We use what are called "Convergence Tests" to determine if a series converges or diverges. The button above will give you a summary of tests that should be memorized. Go up to the menu and click on the subcategory to learn about special convergence cases.
a note about alternating series:
A series whose terms alternate between positive and negative values are called alternating series. Alternating series converge if their signs (positive or negative, usually by a -1 out front) alternate, and the terms themselves are getting smaller.