The AP Calculus BC curriculum includes the study of series of numbers, power series, and various methods to determine convergence or divergence of a series. Students should be familiar with Maclaurin series for common functions and general Taylor series representations. Other topics include the radius and interval of convergence and operations on power series. The technique of using power series to approximate an arbitrary function near a specific value allows for an important connection to the tangent-line problem and is a natural extension that helps achieve a better approximation. The concept of approximation is a common theme throughout AP Calculus, and power series provide a unifying, comprehensive conclusion.

Click on a link to jump ahead to the following sections:

- Lesson 1: Introduction to Sequences
- 4.1 All In a Row - Introduction to Sequences
- 4.12 Introduction to Sequences - TI Nspire lesson to introduce students to sequences on the calculator
- Sequences.tns - Download the .tns file

- Lesson 2: Introduction to Series
- 4.2a Do Plants Know Math? - Arithmetic Series
- 4.2b Geometric Series - Geometric Series
- Defining convergent and divergent infinite series - lesson material on Khan Academy
- Working with geometric series - lesson material on Khan Academy

- Lesson 3: Real Number Series
- 4.3 Are You Divergent? - Series of Real Numbers
- The nth-term test for divergence - lesson material on Khan Academy
- Integral test for convergence - lesson material on Khan Academy
- Harmonic series and p-series - lesson material on Khan Academy
- Comparison tests for convergence - lesson material on Khan Academy

- Lesson 4: Alternating Series
- 4.4 Alternating Series - Alternating Series
- Alternating series test for convergence - lesson material on Khan Academy
- Ratio test for convergence - lesson material on Khan Academy
- Determining absolute or conditional convergence - lesson material on Khan Academy
- Alternating series error bound - lesson material on Khan Academy

- Lesson 5: Taylor and Maclaurin Series
- 4.5 Taylor Series - important uses of Taylor Series
- Finding Taylor polynomial approximations of functions - lesson material on Khan Academy
- Lagrange error bound - lesson material on Khan Academy

- Lesson 6: Power Series
- 4.6 Power Series - important uses of power series
- Radius and interval of convergence of power series - lesson material on Khan Academy
- Finding Taylor or Maclaurin series for a function - lesson material on Khan Academy
- Representing functions as power series - lesson material on Khan Academy

The following are links to resources for Series:

- Big Idea 4 - An overview of the Series module from the College Board
- Infinite sequences and series - Entire unit on Khan Academy

The following are other free resources:

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