Convergence Calculator (Earlier MATLAB Revision)

Script finds the convergence, sum, and partial sum graph of infinite series.

This script is a scaled back version of nfnitcerestst.m, finds the convergence or divergence of infinite series, calculates a sum, and provides a partial sum plot. The tests included are: Divergence Test (nth term test), Ratio Test (d'Alembert ratio test), Root Test (Cauchy root test), Alternating Series Test (Leibniz test), p-Series Test, Geometric Series Test, Raabe's Test, Bertrand's Test, Ermakoff's Test, and Cauchy's Condensation Test. This script will help Calculus (II or III) students with the Infinite Series chapter, Differential Equations students with Series Solutions, and Real Analysis students with Advanced Convergence Tests.

There are 10 convergence tests in total. All the convergence tests require are an infinite series expression input, the test number chosen (from 10), and the starting k. To enter the inputs, answer the questions at the bottom of the command window, after running the script. To the left of the title is a screen shot example of Cauchy's Condensation Test (Theorem and Cauchy's Condensation Test description commented out to fit all information).

I wrote this script because I wanted to enable users of earlier versions of MATLAB, along with owners of less capable machines. My test machine has an older processor, 2 GB RAM, 32 bit Windows 8, and runs R2014a. To run and make nfnitcerestst2.m capable on my test machine, I had to update backwards compatibility. I have researched and tested this script with books on infinite series, internet research, and extensively with ~22 calculus books. If anyone has questions or comments about this script, this includes employment opportunities, feel free to contact me!

[1] Daniel D. Bonar, Michael J. Khoury. "Real Infinite Series." Originally published by The Mathematical Association of America, 2006, Copyright (2006) and reprint (2018) in USA held by American Mathematical Society. Providence, Rhode Island. ISBN: 9781470447823

[2] T. J. IA. Bromwich. "An Introduction to the theory of infinite series." Alpha Editions, www.alphaedis.com (2020). ISBN: 9789354038747