Question
Asked Jan 24, 2020
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What are the Ratio and Root Tests? Do they always give you the information you need to determine convergence or divergence? Give examples.

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Expert Answer

Step 1

A mathematical series can be convergent or divergent subject to certain conditions. Ratio test and the Root test are two of the many tests used to establish the convergent or divergent behaviour of the series.

Step 2

The definition of ratio test is as follows:

Suppose we have a series of the form:

Calculus homework question answer, step 2, image 1

Let us define a limit L such that

 

 

Calculus homework question answer, step 2, image 2
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Step 3

For example suppose we have the following series to test for convergence:

Calculus homework question answer, step 3, image 1

And we want to apply the ratio test to this series, for this we will calculate the limit L as shown below:

...
Calculus homework question answer, step 3, image 2
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