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Chapter 8.5 Alternating Series Saturday, December 08, 2018

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1 Chapter 8.5 Alternating Series Saturday, December 08, 2018
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

2 Chapter 8.5 Alternating Series Saturday, December 08, 2018
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

3 Chapter 8.5 Alternating Series 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Alternating convergent series jump over the sum with each partial sum. The nth partial sum is off by less than the “n+1” jump (the first neglected term) because we know the next jump will jump past the actual sum. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

4 Chapter 8.5 Alternating Series Saturday, December 08, 2018
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

5 Chapter 8.5 Alternating Series 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Actual Sum – Partial Sum = Remainder which is ≤ the first neglected term Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

6 Informal… Chapter 8.5 Alternating Series Saturday, December 08, 2018
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Informal… Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

7 Chapter 8.5 Alternating Series Saturday, December 08, 2018
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

8 Chapter 8.5 Alternating Series Saturday, December 08, 2018
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

9 Chapter 8.5 Alternating Series Saturday, December 08, 2018
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

10 Chapter 8.5 Alternating Series Saturday, December 08, 2018
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

11 Chapter 8.5 Alternating Series 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 1. Determine whether the series converges or diverges using the alternating series test, if possible. 2. Determine if a convergent series converges absolutely or conditionally. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

12 Chapter 8.5 Alternating Series 23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. 1. Determine whether the series converges or diverges using the alternating series test, if possible. 2. Determine if a convergent series converges absolutely or conditionally. Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

13 Practice: Pg. 595 #11-14, 29-30, 69-74 Chapter 8.5 Alternating Series
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges. Practice: Pg. 595 #11-14, 29-30, 69-74 Saturday, December 08, 2018 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals


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