Chapter 9
Infinite Series

Week of February 27
Wednesday, March 1 - Series and Convergence​
Thursday, March 2 - The Integral Test and p-Series
​Friday, March 3 - Direct Comparison and Limit Comparison Test
Week of March 6
Monday, March 6 - Alternating Series and Alternating Series Error Bound
Tuesday, March 7 - Alternating Series and Alternating Series Error Bound
Wednesday, March 8 - Review
Thursday, March 9 - The Ratio Test ​
Friday, March 10 - Quiz
Week of March 13
Monday, March 13 - Taylor Polynomials (UT #1-8)
Tuesday, March 14 - Lagrange Error Bound of a Taylor Polynomial ​
Wednesday, March 15 - Maclaurin Series and Manipulation Involving Substitution
Thursday, March 16 - Manipulation of Taylor Series Involving Integration and Differentiation ​
Friday, March 17 - Geometric Power Series and Interval of Convergence (UT #13-19) 
Week of March 20
Monday, March 20 -  Radius and Interval of Convergence Using Ratio Test (UT #9-12)
Tuesday, March 21 - Review
Wednesday, March 22 - Review
Thursday, March 23 - Test
  • Ch. 9 Test (10 MC and 2 FRQ from ALL of chapter 9​)​
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​Friday, March 24 - Review
  • Go Over Test
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.