A large amount of time in Unit 10 is devoted to convergence tests. These tests tell you under what conditions a series will converge, when the infinite sum will approach a finite number.

The tests are really theorems. As with all theorems, you should learn and understand the hypotheses. This summery of the convergence tests lists the hypotheses of the tests that you are expected to know for the AP Calculus BC exam. The conclusion (at the top) is always that the series will converge or will not converge. You will likely spend a day or two on each test, learning how and when to use it. Use the summary to help you.

Some series have both addition and subtraction signs between the terms (often alternating). A series is said to be absolutely convergent or to converge absolutely if the series of absolute values of its terms converges. In effect, this means you may determine convergence by ignoring the minus signs. If a series converges absolutely, then it converges. This is an important way that many alternating series and series with some minus signs may be tested for convergence. If a series does not converge absolutely, it may still converge. In this case the series are said to be conditionally convergent.

Your goals is to learn which test to use and when to use it.  The short answer is that you may use whichever test works. There is often more than one. Here are two blog posts discussing this. Read these after you’ve learned the convergence tests (but before your teacher’s test). The first post shows how different tests may be used on the same series. The second post gives hints on which test to try first. The key is the standard advice: Practice. Practice. Practice.

Course and Exam Description Unit 10, Sections 10.2 to 10.9. This is a BC only topic.