The integral test is a method for determining whether or not a series defined in of a function diverges or converges. Formally it can be defined as:

For some constant , given a series , where , where is a continuous, positive, and decreasing (or constant) function for , if converges then the series converges. Inversely if the integral diverges then the series also diverges.

Key Rules

For some constant

• , for all
• is decreasing or constant as for every .
• , for every .