Education Technology

Activities

• Subject Area

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

9-12

60 Minutes

• Device
• TI-89 / TI-89 Titanium
• Other Materials
This is Activity 9 from the EXPLORATIONS Book:
Advanced Placement Calculus with the TI-89.

Infinite Sequences and Series - Activity 9

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.

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