Warm Up Chapter 8.1 Sequences 5/7/2019 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. Warm Up 5/7/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Don’t let the new notation confuse you… Chapter 8.1 Sequences 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. Don’t let the new notation confuse you… 𝑓(𝑥) →𝑎(𝑥) →𝑎(𝑛) →𝑎 𝑛 𝑓 𝑥 = 1 𝑥 → 𝑎 𝑛 = 1 𝑛 𝒇 𝒙 𝐢𝐬 𝐜𝐨𝐧𝐭𝐢𝐧𝐮𝐨𝐮𝐬 𝒂 𝒏 𝐢𝐬 𝐝𝐢𝐬𝐜𝐫𝐞𝐭𝐞 ∞ 1 Other notation: 𝑎 𝑛 or simply just 𝑎 𝑛 expanded form: 𝑎 1 , 𝑎 2 , 𝑎 3 ,… 𝑎 𝑛 ,… nth term In our example: 1 𝑛 =1, 1 2 , 1 3 , 1 4 ,…, 1 𝑛 , … 5/7/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Monotonic… Bounded… Chapter 8.1 Sequences 5/7/2019 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. Monotonic… Bounded… 5/7/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.1 Sequences 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. 5/7/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.1 Sequences 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. 5/7/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.1 Sequences 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. 5/7/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.1 Sequences 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. 5/7/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Chapter 8.1 Sequences 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. 5/7/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals

Practice: Pg. 564 #48-58, 67-70, 97-102, 113-116 Chapter 8.1 Sequences 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. 564 #48-58, 67-70, 97-102, 113-116 5/7/2019 ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals