MA 128--Block 8, 2009

COMPUTER LAB 1

In this lab you will experiment with some infinite series. You and your partner should turn in a joint lab report at the beginning of class on Wednesday, April 22. This report should include well-written answers to all questions posed in the lab, and any other observations or questions you think of while working on the lab. Include simple sketches to illustrate geometrical arguments, but you do not need to print web pages or mathematica pages.

1. Go to the website http://math.rice.edu/~lanius/Lessons/Series/infinite.htm. Explain how you can use the pictures to find the sum of the series. Do this with enough detail and clarity that your roommate could follow it.
2. Go to the website http://merganser.math.gvsu.edu/calculus/summation/geometric.html.
1. For the initial r value of ½, click NEXT repeatedly to see what happens. What is the base of the first trapezoid? Second trapezoid? Nth trapezoid? What is the base of the triangle you have at the end? What does this tell you about the sum of the corresponding infinite series?
2. Adjust the r value so that the line intersects the x axis at x=3. Use what you are told about the shaded trapezoid to calculate what this r value must be. Now answer the same questions here as you did for r=1/2 in part a.
3. Answer the questions from part a. for a general value of r. What happens if r is greater than or equal to 1? Do your answers support the claimed result?

Go to: My Computer->Course on Fileserver 1 (J:)->Math->Merrill, then Click on calc2lab1b to open the second half of the lab in the program Mathematica.