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Library AP Calculus AB/BC Unit 10: Infinite Sequences and Series
⁂   AP Calculus AB/BC · Unit 10

10. Infinite Sequences and Series

17–18% of the AP exam. Key topics: Convergence and divergence of sequences, Geometric series: convergence condition and sum formula, p-series: convergence condition, nth-term divergence test, Integral test for convergence, Comparison test and limit comparison test, Ratio test, Alternating series test (AST) and alternating series error bound, Power series and radius/interval of convergence, Taylor series and Maclaurin series, Maclaurin series for e^x, sin x, cos x, 1/(1-x), and ln(1+x), Lagrange error bound for Taylor polynomial approximations.

17–18% exam weight BC track

Unit 10: Infinite Sequences and Series

Study guide content for this unit is being prepared. Check back soon for complete lesson notes, formula sheets, and worked examples.

Topics in this unit

  • Convergence and divergence of sequences
  • Geometric series: convergence condition and sum formula
  • p-series: convergence condition
  • nth-term divergence test
  • Integral test for convergence
  • Comparison test and limit comparison test
  • Ratio test
  • Alternating series test (AST) and alternating series error bound
  • Power series and radius/interval of convergence
  • Taylor series and Maclaurin series
  • Maclaurin series for e^x, sin x, cos x, 1/(1-x), and ln(1+x)
  • Lagrange error bound for Taylor polynomial approximations

Worked FRQ Solutions

Free-response questions from past AP exams that test this unit's concepts.