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## Convergence Calculator for Infinite Series & Power Series

version 1.5.4 (46.5 KB) by
This script finds the convergence, sum, partial sum graph, radius and interval of convergence, of infinite series.

62 Downloads

Updated 25 Sep 2020

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This script determines the convergence or divergence of infinite series, calculates a sum, provides a partial sum plot, and calculates radius and interval of convergence of power series. The tests included are: Divergence Test (nth term test), Integral Test (Maclaurin-Cauchy test), Comparison Test, Limit Comparison Test, Ratio Test (d'Alembert ratio test), Root Test (Cauchy root test), Alternating Series Test (Leibniz test), Absolute Convergence Test, p - Series Test, Geometric Series Test, Raabe's Test, and Power Series Test. The Power Series Test uses the ratio test, the root test, and the Cauchy-Hadamard theorem to calculate the radius and interval of convergence. This script may help the Calculus (II or III) student with the Infinite Series chapter, and it may also help the Differential Equations student with Series Solutions.

### Cite As

David Cazenave (2020). Convergence Calculator for Infinite Series & Power Series (https://www.mathworks.com/matlabcentral/fileexchange/72141-convergence-calculator-for-infinite-series-power-series), MATLAB Central File Exchange. Retrieved .

### Comments and Ratings (15)

sammy jang

Anthony Mendez

Thank you for taking the time to put this together. I am a Calculus 3 student and while this is not always correct, as you, the author clearly states, this has been instrumental is saving me a bunch of time in validating my work. Not all heroes wear capes.

David Cazenave

Hello Sia. The Limit Comparison Test requires you to enter the series expression, test # 4, starting k, c or d, and comparison expression. The answer then appears.

Sia Sheth

For the limit comparison test am I supposed to give the series to be compared with as well? After inputting starting k as 2, I got a detailed explanation of what the limit comparison test is but no answer given. I was also then asked whether this series converges (c) or diverges (d) - I believed that was what your code would answer for me.

David Cazenave

If you don't know what my script is for, or you can't figure out how to use it, maybe you should find another mfile.

Lester Mendigoria

How do i actually uses this?

David Cazenave

I have five star ratings from 2 Mathworks staff members.

David Cazenave

MATLAB has a specific way that you have to enter input. It's called syntax. All programming languages have syntax. All mfiles run with the same syntax.

Zied Almasri

Good idea. but there simply needs to be a tutorial for how to enter things properly. I can't even tell if the calculator works because 90% of the time it has a input error.

Alisa Shafira

could you please give me a tutorial to use the calculator?

David Cazenave

Hello Mohamad and thank you for your interest in my script! For an example, click on the screenshot to the left of the file title above.

can i get example to input a question ?

Jaime Pintor

Gunjan Jhawar

### Updates

 25 Sep 2020 1.5.4 Strengthened filters in the Absolute Convergence Test with the Integral Test, and the Alternating Series Test. Changed some display statements in the Limit Comparison Tests. 9 Sep 2020 1.5.3 Fixed bug in the Absolute Convergence Test with the Integral Test. Fixed bug in the Integral Test. Reorganized display statement blocks in the 4 comparison tests. 24 Aug 2020 1.5.2 Strengthened a filter in the Absolute Convergence Test with the Integral Test. Clarified a display statement block in the 4 comparison tests. 13 Aug 2020 1.5.1 Expanded logarithmic capability of both Integral Tests, both Comparison Tests, and both Limit Comparison Tests. Expanded capability of the p-Series Test and the Geometric Series Test. Improved robustness of the Power Series Test. 1 May 2020 1.5.0 Improved trigonometric capability of the Absolute Convergence Test with the Integral Test, and the Alternating Series Test. Adjusted Limit Comparison Test plot marker color. Fixed bug in Divergence Test, and fixed bug in Alternating Series Test. 14 Apr 2020 1.4.9 Added comments to both Integral Tests, and added display statements to the descriptions of both Comparison Tests. 11 Apr 2020 1.4.8 Improved robustness of Raabe's Test and added comments to the Integral Tests. 11 Mar 2020 1.4.7 Expanded trigonometric capability of the Absolute Convergence Test with the Integral Test and the Absolute Convergence Test with the Comparison Test. 2 Mar 2020 1.4.6 Corrected error in Alternating Series Test and Raabe's Test. 22 Feb 2020 1.4.5 Fixed bug in Raabe's Test. 21 Feb 2020 1.4.4 Improved robustness of, and added a comment to Raabe's Test. 17 Feb 2020 1.4.3 Fixed bug in the Absolute Convergence Test with the Integral Test, and fixed bug in the Power Series Test. 23 Jan 2020 1.4.2 Corrected a variable name and deleted a comment. 8 Jan 2020 1.4.1 Improved robustness of the Power Series Test. 3 Jan 2020 1.4.0 Improved robustness of Raabe's Test. 1 Jan 2020 1.3.9 Nested 6 if statements and deleted extraneous code in the Power Series Test. 27 Dec 2019 1.3.8 Improved robustness of Raabe's Test, added some display statements to the Integral Test description, and switched display statements between the Comparison Test and the Absolute Convergence Test with the Comparison Test. 10 Dec 2019 1.3.7 Improved robustness of the Absolute Convergence Test with the Integral Test and updated Required MathWorks Products. 5 Dec 2019 1.3.6 Improved robustness of Raabe's Test and added some display statements to the Comparison Test and the Absolute Convergence Test with the Integral Test descriptions. 18 Nov 2019 1.3.5 Improved robustness of the Integral Test, Comparison Test, Limit Comparison Test, Ratio Test, Root Test, Absolute Convergence Tests, p - Series Test, and Raabe's Test. 13 Nov 2019 1.3.4 Changed Summary. 11 Nov 2019 1.3.3 Updated screenshot, added to Overview description, and modified comments description. 8 Nov 2019 1.3.2 Changed the Overview and added a couple of display statements. 2 Nov 2019 1.3.1 Changed when series_expr_integral is displayed in the Absolute Convergence Test with the Integral Test. 22 Oct 2019 1.3.0 Added some display statements to the Absolute Convergence Test with the Comparison Test description, the Absolute Convergence Test with the Limit Comparison Test description, and the Power Series Test description. 17 Oct 2019 1.2.9 Corrected punctuation in a couple of display statements. 14 Oct 2019 1.2.8 Improved robustness, deleted and added some code, and added some comments. 11 Oct 2019 1.2.7 Improved robustness and added some display statements. 5 Oct 2019 1.2.6 Fixed bug with the Power Series Test. 3 Oct 2019 1.2.5 Improved robustness of the Power Series Test. 1 Oct 2019 1.2.4 Added some comments and to Power Series Test description. 24 Sep 2019 1.2.3 Expanded capability and improved robustness of the Power Series Test, also updated the Integral Test, Ratio Test, Root Test, Alternating Series Test, Absolute Convergence Test with the Integral Test, Raabe's Test, and some descriptions. 30 Aug 2019 1.2.2 Deleted some extraneous code. 30 Aug 2019 1.2.1 Fixed bug with the Power Series Test. 29 Aug 2019 1.2.0 Increased capability of the Power Series Test. 24 Aug 2019 1.1.9 Clarified some display statements and corrected bug with the Power Series Test. 21 Aug 2019 1.1.8 Improved robustness of the Power Series Test. 17 Aug 2019 1.1.7 Improved robustness and speed. 17 Aug 2019 1.1.6 Fixed bug with the Power Series Test. 13 Aug 2019 1.1.5 Corrected Power Series Test description. 12 Aug 2019 1.1.4 Corrected Absolute Convergence Test with the Integral Test description and expanded trigonometric capability of the Power Series Test. 5 Aug 2019 1.1.3 Corrected error with Absolute Convergence Test sums and their partial sum graphs, and expanded capability. 2 Aug 2019 1.1.2 Corrected comments description. 1 Aug 2019 1.1.1 Modified script summary and description. 30 Jul 2019 1.1.0 Changed an elseif to an else. 29 Jul 2019 1.0.9 Corrected comments description and improved robustness. 25 Jul 2019 1.0.8 Updated MATLAB Release Compatibility. 23 Jul 2019 1.0.7 Deleted some display statements and added a comments description. 19 Jul 2019 1.0.6 Corrected display statement. 19 Jul 2019 1.0.5 Resubmission. 16 Jul 2019 1.0.4 Improved robustness. 15 Jul 2019 1.0.3 Modified screenshot again. 15 Jul 2019 1.0.2 Modified screenshot. 15 Jul 2019 1.0.1 Changed title and added screenshot.
##### MATLAB Release Compatibility
Created with R2019a
Compatible with R2013b to any release
##### Platform Compatibility
Windows macOS Linux