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

9-2 Series and Convergence

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

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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

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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

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Theorem 9.7 Properties of Infinite Series

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Theorem 9.8 Limit of nth Term of a Convergent Series

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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

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