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Convergence Calculator for Infinite Series & Power Series

version 1.3.7 (41.2 KB) by David Cazenave
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 .

Comments and Ratings (4)

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 ?

Updates

1.3.7

Improved robustness of the Absolute Convergence Test with the Integral Test and updated Required MathWorks Products.

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.

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.

1.3.4

Changed Summary.

1.3.3

Updated screenshot, added to Overview description, and modified comments description.

1.3.2

Changed the Overview and added a couple of display statements.

1.3.1

Changed when series_expr_integral is displayed in
the Absolute Convergence Test with the Integral Test.

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.

1.2.9

Corrected punctuation in a couple of display statements.

1.2.8

Improved robustness, deleted and added some code, and added some comments.

1.2.7

Improved robustness and added some display statements.

1.2.6

Fixed bug with the Power Series Test.

1.2.5

Improved robustness of the Power Series Test.

1.2.4

Added some comments and to Power Series Test description.

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.

1.2.2

Deleted some extraneous code.

1.2.1

Fixed bug with the Power Series Test.

1.2.0

Increased capability of the Power Series Test.

1.1.9

Clarified some display statements and corrected bug with the Power Series Test.

1.1.8

Improved robustness of the Power Series Test.

1.1.7

Improved robustness and speed.

1.1.6

Fixed bug with the Power Series Test.

1.1.5

Corrected Power Series Test description.

1.1.4

Corrected Absolute Convergence Test with the Integral Test description
and expanded trigonometric capability of the Power Series Test.

1.1.3

Corrected error with Absolute Convergence Test sums
and their partial sum graphs, and expanded capability.

1.1.2

Corrected comments description.

1.1.1

Modified script summary and description.

1.1.0

Changed an elseif to an else.

1.0.9

Corrected comments description
and improved robustness.

1.0.8

Updated MATLAB Release Compatibility.

1.0.7

Deleted some display statements
and added a comments description.

1.0.6

Corrected display statement.

1.0.5

Resubmission.

1.0.4

Improved robustness.

1.0.3

Modified screenshot again.

1.0.2

Modified screenshot.

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