Simple convergence/divergence test for a series for the TI-83

By Justin B. Michaels
justinbmichaels@hotmail.com

This program allows you to easily test the summation of a series for convergence or divergence. Simply enter the equation for the series into Y1 in function mode in terms of x (example: Y1=1/(10^x)). Next, run the program. You will be prompted for a start value and end value. Start value is usually 1, however, some ln() functions require a start value greater than 1. For the end value, convergence/divergence can usually be ascertained by the time x=50, however this is not true for all functions. After you enter the end value, the program will begin to run. On the top line of the screen, the current x-value ('n' in summation parlance) is displayed. On the second line, the sum of the series is displayed. In order to determine if your series converges or diverges, you must watch the summation total as it grows. I have found that if the series is converging, this value will *usually* stop growing by the time an end value of 50 is reached. If the series is diverging, the summation total will continue to grow and will not approach any limit. Also, if the sum of the series can be converted into a fraction, this program will do so at the end of execution (almost a sure sign your summation series converges). This prog is good for checking your answers after applying a convergence/divergence test in calc II.