Chapter 9
Infinite Series

Week of February 28
Monday, February 28 - Series and Convergence​
Tuesday, March 1 - The Integral Test and p-Series
​Wednesday, March 2 - Review 
Thursday, March 3 - Limit Comparison Test ​
Friday, March 4 - Alternating Series Introduction
Week of March 7
Monday, March 7 - Alternating Series Error Bound
  • 9.5 #27, 29, 31, 35​, 37-53 odd, 63

Tuesday, March 8 - Review
Wednesday, March 9 - The Ratio Test
Thursday, March 10 - Review ​
Friday, March 11 - Quiz
Week of March 14
Monday, March 14 - Taylor Polynomials (UT #1-8)
Tuesday, March 15 - Lagrange Error Bound of a Taylor Polynomial ​
Wednesday, March 16 - Maclaurin Series and Manipulation Involving Substitution
Thursday, March 17 - Manipulation of Taylor Series Involving Integration and Differentiation ​
Friday, March 18 - Manipulation of Taylor Series Involving Integration and Differentiation
Week of March 21
Monday, March 21 -  Geometric Power Series and Interval of Convergence (UT #13-19) 
Tuesday, March 22 - Radius and Interval of Convergence Using Ratio Test (UT #9-12)
Wednesday, March 23 - Review
Thursday, March 24 - Review
​Friday, March 25 - Test
  • Ch. 9 Test (10 MC and 2 FRQ from ALL of chapter 9​)​
AP Standards for Chapter 9
Concept of series (Section 9.2)
  • A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence and divergence.
Series of constants (Sections 9.2-9.6)
  • Motivating examples, including decimal expansion.
  • Geometric series with applications. (9.2)
  • The harmonic series. (9.3)
  • Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series. (9.3)
  • Comparing series to test for convergence or divergence. (9.4)
  • Alternating series with error bound. (9.5)
  • The ratio test for convergence and divergence. (9.6)
Taylor series (Sections 9.7-9.10)
  • Taylor polynomial approximation with graphical demonstration of convergence (for example, viewing graphs of various Taylor polynomials of the sine function approximating the sine curve).
  • Lagrange error bound for Taylor polynomials.
  • Maclaurin series and the general Taylor series centered at x = a.
  • Maclaurin series for the functions sin, cos, e^x, and 1/(1-x)
  • Formal manipulation of Taylor series and shortcuts to computing Taylor series, including substitution, differentiation, antidifferentiation, and the formation of new series from known series.
  • Functions defined by power series.
  • Radius and interval of convergence of power series.