ap calculus objective: understand definition of convergent infinite series and use properties of...
TRANSCRIPT
9-2 Series and Convergence
AP Calculus Objective: Understand definition of convergent infinite series and use properties of infinite geometric series.
Copyright © Houghton Mifflin Company. All rights reserved. 9-
2
Definitions of Convergent and Divergent Series
Convergent and Divergent Series
Convergent and Divergent Series
A telescoping series is a series whose partial sums eventually only have a fixed number of terms after cancellation (b1-b2)+(b2-b3)+(b3-b4)+…
Find the sum of the series
Writing a Series in Telescoping Form
Copyright © Houghton Mifflin Company. All rights reserved. 9-
6
Theorem 9.6 Convergence of a Geometric Series
Geometric Series
Convergent and Divergent Geometric Series
Use a geometric series to write as the ratio of two numbers.
A Geometric Series for a Repeating Decimal
Use a geometric series to write as the ratio of two numbers.
A Geometric Series for a Repeating Decimal
Copyright © Houghton Mifflin Company. All rights reserved. 9-
10
Theorem 9.7 Properties of Infinite Series
Copyright © Houghton Mifflin Company. All rights reserved. 9-
11
Theorem 9.8 Limit of nth Term of a Convergent Series
Copyright © Houghton Mifflin Company. All rights reserved. 9-
12
Theorem 9.9 nth-Term Test for Divergence
a. b. c.
Using the n-th Term Test for Divergence
A ball is dropped from a height of 6 feet and begins bouncing. The height of each bounce is ¾ the height of each previous bounce. Find the total vertical distance traveled by the ball.
Bouncing Ball Problem
Page 614 #9, 12, 17, 18, 37, 39, 43, 45, 51, 59, 61, 68, 69, 70, 71, 72, 74
Classwork/Homework