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AP Calculus BC Unit 10: Infinite Sequences and Series
Target the BC-only series unit with convergence tests, Taylor series intuition, and high-yield AP-style review.
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What this unit covers
18 lessons, each with worked examples, practice problems and flashcards.
Sequences & Series
- Infinite Sequences
Sequence basics, convergence, bounded/monotonic sequences, and limits
- Infinite Series
Geometric series, telescoping series, nth term test, and harmonic series
- Convergence Tests Summary
Direct comparison, limit comparison, ratio test, root test, and choosing tests
- Alternating Series
Alternating series test, error bound, conditional vs absolute convergence
Power Series & Taylor/Maclaurin
- Power Series
Power series basics, radius and interval of convergence, differentiation and integration
- Taylor & Maclaurin Series
Taylor series, Maclaurin series, common series, and Taylor polynomials
- Lagrange Error Bound
Error bound formula, finding maximum error, choosing polynomial degree
- Series Applications
Function approximation, solving DEs with series, physics applications, and error analysis
Sequences & Series (BC)
- Introduction to Sequences
Understanding sequences and their behavior
- Introduction to Infinite Series
Understanding infinite series and partial sums
- The Integral Test
Using integrals to test series convergence
- Direct and Limit Comparison Tests
Comparing series to determine convergence
- Alternating Series Test
Testing convergence of alternating series
- Ratio and Root Tests
Testing convergence with ratios and roots
Power & Taylor Series (BC)
- Introduction to Power Series
Understanding power series and their properties
- Radius and Interval of Convergence
Finding where power series converge
- Taylor and Maclaurin Series
Representing functions as infinite series
- Common Taylor Series and Applications
Key series formulas and how to use them
Common questions
- What does AP Calculus BC Unit 10: Infinite Sequences and Series cover?
- 18 lessons across 4 areas: Sequences & Series, Power Series & Taylor/Maclaurin, Sequences & Series (BC), Power & Taylor Series (BC).
- Is AP Calculus BC Unit 10: Infinite Sequences and Series free to study?
- Yes. Every lesson, quiz and set of flashcards on this page is free to use.
- Where should I start?
- Take the diagnostic first so you know which lessons in this unit you can skip, then work the rest in order and finish each with its exit quiz.