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AP Calculus Objective: Understand definition of convergent infinite series and use properties of infinite geometric series.

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Presentation on theme: "AP Calculus Objective: Understand definition of convergent infinite series and use properties of infinite geometric series."— Presentation transcript:

1 AP Calculus Objective: Understand definition of convergent infinite series and use properties of infinite geometric series.

2 Copyright © Houghton Mifflin Company. All rights reserved. 9-2

3

4 A telescoping series is a series whose partial sums eventually only have a fixed number of terms after cancellation (b 1 -b 2 )+(b 2 -b 3 )+(b 3 -b 4 )+…

5 Find the sum of the series

6 Copyright © Houghton Mifflin Company. All rights reserved. 9-6 Geometric Series

7

8 Use a geometric series to writeas the ratio of two numbers.

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10 Copyright © Houghton Mifflin Company. All rights reserved. 9-10

11 Copyright © Houghton Mifflin Company. All rights reserved. 9-11

12 Copyright © Houghton Mifflin Company. All rights reserved. 9-12

13 a.b.c.

14 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.

15  Page 614 #9, 12, 17, 18, 37, 39, 43, 45, 51, 59, 61, 68, 69, 70, 71, 72, 74


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