1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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, ,
5/7/2019
ESLR -Tracy High Graduates will be Independent Learners Who Set realistic and challenging goals