Chapter 9
Infinite Series

Week of February 18
Monday, February 18 - No School
  • Midwinter Break

Tuesday, February 19 - Series and Convergence (UT #1-11)​
​Wednesday, February 20 - The Integral Test and p-Series (UT #12-14)
Thursday, February 21 - Review Day
  • 9.2 #7-19 odd, 25-35 odd, 41-49 odd
  • 9.3 #1, 3, 7, 13, 25-37 odd, 71-81 odd
​
Friday, February 22 - Comparison of Series (Direct and Limit) (UT #15-23)
Week of February 25
Monday, February 25 - Alternating Series Introduction (UT #24-30)
Tuesday, February 26 - Alternating Series Error Bound
  • 9.5 #27, 29, 31, 35

Wednesday, February 27 - The Ratio Test (UT #31-36)
Thursday, February 28 - Review ​
Friday, March 1 - Quiz
  • Quiz 9.2-9.6
Week of March 4
Monday, March 4 - Taylor Polynomials (UT #1-8)
Tuesday, March 5 - Continue Taylor Polynomials
Wednesday, March 6 - Lagrange Error Bound of a Taylor Polynomial
Thursday, March 7 - Maclaurin Series and Manipulation Involving Substitution (UT #20-27)  ​
Friday, March 8 - Manipulation of Taylor Series Involving Integration and Differentiation
Week of March 11
Monday, March 11 -  Manipulation of Taylor Series Involving Integration and Differentiation
Tuesday, March 12 - Geometric Power Series and Interval of Convergence (UT #13-19) 
Wednesday, March 13 - Radius and Interval of Convergence Using Ratio Test (UT #9-12)
Thursday, March 14 - Review​​​
​Friday, March 15 - Review
Week of March 18
Monday, March 18 - Review
Tuesday, March 19 - Review
Wednesday, March 20 - 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.