Infinite Sequences and Series

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Calculus: Applications of Integral, Antiderivatives and Definite Integrals

Math: AP Calculus: AP Calculus

Level

9-12

Activity Time

60 Minutes

TI Calculator

TI-89 / TI-89 Titanium

Resource Types

Lessons

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Infinite Sequences and Series

Activity Overview

In this activity, students investigate and learn about functions known as sequences. They learn how they can be represented symbolically, graphically, and numerically.

Before the Activity

See the attached PDF file for detailed instructions for this activity

Print pages 79 - 86 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:
Investigating Sequences Numerically, Graphically and Symbolically:

Use the seq (sequence) command to look at the sequence numerically

Graph the sequence to examine its behavior and use the limit command to evaluate the sequence symbolically

Convergence of an Infinite Series:

Use the ratio test to establish the convergence of the infinite series

Enter the expression for the n th partial sum and observe values in a table

Estimate the sum of the infinite series

Taylor Series:

Define the functions f(x) and p(x)

Equate the first and second order derivatives to calculate the coefficient of P(x)

Graph the 2 functions

Generate the polynomial using the Taylor command

Integral of Taylor Polynomial:
use the taylor command and observe two results

After the Activity

Students will complete the practice exercise problems.

Review student results:

As a class, discuss questions that appeared to be more challenging

Re-teach concepts as necessary

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes Appendix A PDF Teacher Notes Appendix B PDF Teacher Notes Appendix C PDF Teacher Notes Appendix D PDF Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Calculus: Applications of Integral, Antiderivatives and Definite Integrals

Math: AP Calculus: AP Calculus

Level

9-12

Activity Time

60 Minutes

TI Calculator

TI-89 / TI-89 Titanium

Resource Types

Lessons

Report an Issue

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Infinite Sequences and Series

Infinite Sequences and Series

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