# Activities

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• • ##### Subject Area

• Math: Precalculus: Other Topics: Matrices, Sequences, and Series

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• TI-Nspire™ Apps for iPad®
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.6

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Sum of Infinite Geometric Series

#### Activity Overview

This lesson involves clicking on a slider to see that the area of a square that has been systematically divided into an infinite number of pieces approaches 1.

#### Objectives

• Students will understand how a unit square can be divided into an infinite number of pieces.
• Students will understand a justification for the following theorem: The sum of the infinite geometric series 1/2 + 1/4 + 1/8 + 1/16 + ... = 1.
• Students will be able to explain why the sum of an infinite geometric series is a finite number if and only if |r| < 1.

#### Vocabulary

• geometric series
• infinite series
• ratio of a geometric series
• sigma notation

#### About the Lesson

This lesson involves clicking on a slider to see that the area of a square that has been systematically divided into an infinite number of pieces approaches 1.
As a result, students will:

• Connect the area of a square with the sum of the series 1/2 + 1/4 + 1/8 + 1/16... and realize that the sum is 1.
• Examine several infinite geometric series with various ratios to determine that the sum of an infinite geometric series is a finite number if and only if |r|<1.