Unit 3: Chapter 11 - Infinite Sequences and Series
Duration of Days: 29
Students will know the following:
- The difference between a sequence and a series
- Whether a sequence or series converges or diverges using various methods
- How to determine the sum (or an estimate within a given error) of a convergent series
- How to represent a function as a power series
- How to represent a function as a Taylor or Maclaurin Series
Students will find formulas for sequences in terms of n and define recursively, determine whether a sequence converges or diverges, learn various methods for determining whether a series converges or diverges, determine the exact sum or an estimate of the sum of a convergent series, and represent functions as a Power Series, Taylor Series, or Maclaurin Series.
Students will demonstrate their learning of sequences and series through formative and summative assessments, class discussions, and class work.
| Lesson # | Lesson Title | Duration of Days |
|---|---|---|
| 1 | 11.1 Sequences | 3 |
| 2 | 11.2 Series | 4 |
| 3 | 11.3 The Integral Test and Estimates of Sums | 3 |
| 4 | 11.4 The Comparison Tests | 3 |
| 5 | 11.5 Alternating Series | 2 |
| 6 | 11.6 Absolute Convergence and the Ratio and Root Tests | 3 |
| 7 | 11.7 Strategy for Testing Series | 2 |
| 8 | 11.8 Power Series | 3 |
| 9 | 11.9 Representations of Functions as Power Series | 2 |
| 10 | 11.10 Taylor and Maclaurin Series | 4 |