Education Technology

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.

    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