Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Series and Taylor Polynomials

College

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-89 / TI-89 Titanium

TI Connect™

• ##### Accessories

TI Connectivity Cable

## Exploring Taylor Series

#### Activity Overview

In this Computer Algebra System (CAS) activity, students explore the Taylor's series. They investigate the approximation of numbers in sequences and series and find their interval of convergence using various methods.

#### Before the Activity

• Install TI Connect™ using the TI connectivity cable
• See the attached PDF file for detailed instructions for this activity
• Print pages 1 - 22 from the attached PDF file for the class
• #### During the Activity

Distribute the pages to the class.

• Enter a sequence in different modes
• Examine an alternating series and describe its pattern
• Study an alternating series and approximate it after filling in the distances given by each arrow on the activity sheet

• Understand the concept of conditional convergence
• Realize that any conditionally convergent series can be rearranged to add up to any given number

• Set the window range and plot the graphs of the given functions
• Solve various approximation problems involving different series, provided on the activity sheet
• Use Taylor approximations to solve problems involving series
• Write the first four terms of the given series, and state the interval of convergence
• Write the series for an expression, and find the interval for convergence using substitution
• Differentiate and integrate both sides of the series
• Solve various problems involving Maclaurian series and intervals of convergence

• Use series to evaluate the limits of a function and verify the result with the help of L-Hospital's rule
• #### After the Activity

Students answer questions on the Activity sheet.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary