Determining the Best Convergence Test to Apply
Learn how to identify the best convergence test for an infinite series, including the nth-term test, geometric series, p-series, integral test, comparison tests, limit comparison, alternating series, and ratio test.
Defining Convergent and Divergent Infinite Series
Learn how to define convergent and divergent infinite series using partial sums, limits, and the precise meaning of convergence for AP Calculus AB & BC.
Constructing Taylor Polynomials Centered at a Value
Learn how to construct Taylor polynomials centered at a value, with the general formula, step-by-step methods, and fully worked AP Calculus BC examples.
Comparison Tests for Convergence
Learn how to use the Direct Comparison Test and Limit Comparison Test to determine whether an infinite series converges or diverges in AP Calculus BC.
Alternating Series and the Alternating Series Test
Learn how alternating series work and how to use the Alternating Series Test to determine convergence, with step-by-step examples for AP Calculus BC.
Alternating Series Error Bound
How to use the Alternating Series Error Bound to estimate the error in an alternating series approximation, with step-by-step AP Calculus AB & BC examples.
Absolute vs. Conditional Convergence
Learn the difference between absolute and conditional convergence, how to test each type of convergence, and how the alternating series test and comparison tests fit together for AP Calculus BC.