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## Convergence Calculator for Infinite Series & Power Series

version 1.3.7 (41.2 KB) by David Cazenave

### David Cazenave (view profile)

This script finds the convergence, sum, partial sum graph, radius and interval of convergence of infinite series.

125 Downloads

Updated 10 Dec 2019

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This script determines the convergence or divergence of infinite series, calculates a sum, provides a partial sum graph, 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 (2019). 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 .

David Cazenave

### David Cazenave (view profile)

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.

Mohamad Alvarez Reyzal Khastubi

### Mohamad Alvarez Reyzal Khastubi (view profile)

can i get example to input a question ?

Jaime Pintor

Gunjan Jhawar

### Updates

 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