1. Intro to Infinite Series Geometric Series
Lesson 8.2

2. Definition of Series
Consider summing the terms of an infinite sequence
We often look at a partial sum of n terms

3. View Spreadsheet Example
Definition of Series
We can also look at a sequence of partial sums { Sn }
The series can converge with sum S
The sequence of partial sums converges
If the sequence { Sn } does not converge, the series diverges and has no sum
View Spreadsheet Example

4. Examples
Convergent
Divergent

5. Telescoping Series Consider the series Represent as partial fraction
Expand
Regroup
Telescope and evaluate

6. Properties of Infinite Series
Linearity
The series of a sum = the sum of the series
Use the property

7. View Spreadsheet Example (Again)
Geometric Series
View Spreadsheet Example (Again)
Definition
An infinite series
The ratio of successive terms in the series is a constant
Example
What is r ?

8. Geometric Series Theorem
Given geometric series (with a ≠ 0)
Series will
Diverge when | r | ≥ 1
Converge when | r | < 1
Examples
Compound interest Or

9. Assignment A
Lesson 8.2A
Page 511
Exercises 5 – 29 odd

10. Apply to Repeating Decimals
Given repeating decimal
Consider this as repeating part of the decimal is a geometric series
What is the a? The r ?

11. Apply to Repeating Decimals
Rewrite
Apply formula for sum of geometric series
Combine

12. Applications
A pendulum is released through an arc of length 20 cm from vertical
Allowed to swing freely until stop, each swing 90% as far as preceding
How far will it travel until it comes to rest?
20 cm

13. Assignment B
Lesson 8.2B
Page 512
Exercises 31, 33, 35, – 55 odd