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 cableSee 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.
Follow the Activity procedures:
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