Step 1: Build the convergence foundationReview the definition of convergence via partial sums, work through telescoping and geometric series examples, and practice the nth term test. Confirm you know when each test is conclusive versus inconclusive.
Step 2: Work through the convergence test toolkitPractice the integral test, p-series rule, direct and limit comparison tests, alternating series test, and ratio test in sequence. For each test, write out the conditions, apply the test, and state the conclusion. Use the topic guides for Topics 10.4 through 10.9.
Step 3: Practice absolute and conditional convergence and error boundsClassify series as absolutely or conditionally convergent. Then practice the alternating series error bound and the Lagrange error bound side by side, focusing on how to choose M and how to write interval estimates.
Step 4: Build and manipulate Taylor and Maclaurin seriesMemorize the five standard Maclaurin series. Practice building Taylor polynomials from derivative tables. Then derive series for new functions using substitution, multiplication, term-by-term differentiation, and term-by-term integration.
Step 5: Consolidate with power series and FRQ practicePractice finding the radius and interval of convergence, including endpoint tests. Work through FRQ practice problems that combine series identification, error bounds, and series manipulation in multi-part problems. Use the AP score calculator to estimate your score range.