integral test

American  

noun

Mathematics.

1. the theorem that a given infinite series converges if the function whose value at each integer is the corresponding term in the series is decreasing, tends to zero, and results in a finite number when integrated from one to infinity.

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Example Sentences

This test, called the integral test, compares an infinite sum to an improper integral.

From Textbooks • Mar. 30, 2016

We have seen that the integral test allows us to determine the convergence or divergence of a series by comparing it to a related improper integral.

From Textbooks • Mar. 30, 2016

For each of the following series, use the integral test to determine whether the series converges or diverges.

From Textbooks • Mar. 30, 2016

For some types of series, we are able to use the ideas from the integral test to estimate RN.

From Textbooks • Mar. 30, 2016

To illustrate how the integral test works, use the harmonic series as an example.

From Textbooks • Mar. 30, 2016