|
The AMATYC Review Fall 2005, Vol.27, No.1 |
Classroom Issues with Series Tests Jawad Sadek and Russell Euler |
 |
Jawad Sadek is an associate professor of mathematics at Northwest Missouri State University in Maryville. His main interests include complex analysis, problem solving, his students' questions, and soccer. E-mail: jawads@mail.nwmissouri.edu Russell Euler is a professor in the Department of Mathematics and Statistics at Northwest Missouri State University. His interests include analysis, geometry, and number theory. Presently he is the Problems Editor for the Elementary Problems and Solutions section of The Fibonacci Quarterly. E-mail: reuler@mail.nwmissouri.edu |
| We find infinite series in calculus to be one of the most confusing topics our students encounter. In this note, we look at some issues that our students find difficult or ambiguous involving the Ratio Test, the Root Test, and also the Alternating Series Test. We offer some suggestions and some examples, which could be a supplement to the set of the exercises in the standard calculus texts, to help alleviate these difficulties. Precisely, we discuss the issue of the relationship between the Ratio Test and the Root Test as well as some misconceptions that students may have when applying the Alternating Series Test. In particular, students often fail to understand the importance of checking that the sequence is nonincreasing. We also point out how they may even confuse the concept of alternating terms. | |