1. Power Series, Interval of Convergence
Chapter 9.8
Power Series, Interval of Convergence
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.
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

2. Power Series, Interval of Convergence
Chapter 9.8
Power Series, Interval of Convergence
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.
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

3. For what value(s) of x does the power series converge?
Chapter 9.8
Power Series, Interval of Convergence
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.
For what value(s) of x does the power series converge?
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

4. Informal investigation:
Chapter 9.8
Power Series, Interval of Convergence
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 investigation:
For what value(s) of x does the power series converge?
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

5. Informal investigation:
Chapter 9.8
Power Series, Interval of Convergence
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 investigation:
For what value(s) of x does the series converge?
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

6. Ratio Test Chapter 9.8 Power Series, Interval of Convergence 4/20/2019
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.
Ratio Test
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

7. For what value(s) of x does the power series converge?
Chapter 9.8
Power Series, Interval of Convergence
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.
For what value(s) of x does the power series converge?
Radius of convergence
Centered at x=0
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

8. Power Series, Interval of Convergence
Chapter 9.8
Power Series, Interval of Convergence
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.
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

9. Remember that the ratio test is inconclusive when the ratio = 1.
Chapter 9.8
Power Series, Interval of Convergence
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.
MUST PLUG IN ENDPOINTS AND CHECK TO SEE IF x=1 or x=3 cause convergence or divergence.
Remember that the ratio test is inconclusive when the ratio = 1.
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

10. Power Series, Interval of Convergence
Chapter 9.8
Power Series, Interval of Convergence
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.
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

11. Power Series, Interval of Convergence
Chapter 9.8
Power Series, Interval of Convergence
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.
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

12. Power Series, Interval of Convergence
Chapter 9.8
Power Series, Interval of Convergence
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.
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

13. Power Series, Interval of Convergence
Chapter 9.8
Power Series, Interval of Convergence
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.
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

14. Power Series, Interval of Convergence
Chapter 9.8
Power Series, Interval of Convergence
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.
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

15. Practice: Chapter 9.8 Power Series, Interval of Convergence 4/20/2019
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:
4/20/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals