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Convergence Calculator

version 1.5.9 (46.6 KB) by David Cazenave
This script finds the convergence, sum, partial sum graph, radius and interval of convergence, of infinite series.


Updated 04 Dec 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 (2021). Convergence Calculator (, 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

MATLAB Release Compatibility
Created with R2019a
Compatible with R2013b and later releases
Platform Compatibility
Windows macOS Linux

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