# Science:Infinite Series Module/Units/Unit 2/2.2 The Integral Test/2.2.09 Final Thoughts on The Integral Test

The previous lesson on the divergence test gave us a way of determining whether some infinite series diverge. We saw that the divergence test had a limitation: it can tell us if certain infinite series diverges, but it cannot tell us if a given series converges. But there are other convergence tests. The integral test, for example, provides a test for any series

whose terms *a _{n}* can be related to a continuous, positive, decreasing function. Essentially, we let , then evaluate the integral

and:

- if the integral
**converges**, the infinite series**converges**, and - if the integral
**diverges**, the infinite series**diverges**.

Although this test is limited to functions who are continuous, positive and decreasing, we saw that it led us to a useful convergence theorem for any infinite series of the form