If you want a series test that is only applied under one very specific condition – leaving no doubt as to what test you should choose – this is it!
Understanding the Root Test
If you are asked to test the convergence of a series where you are given a variable raised to a variable, then look no further than the Root Test.
It is perfectly designed to handle this type of form or scenario and will enable us to quickly apply a limit approaching infinity, and draw conclusions as to absolute convergence that are striking similarities to it’s counterpart, the Ratio Test.
Most importantly, the Root Test is used when we are given a series containing the definition of “e“. Wikipedia defines Euler’s number, e, as the important mathematical constant that is the base of the natural logarithm and is used in the study of compound interest.
Together we will explore this definition and see how we can use our knowledge of the Root Test to determine absolute convergence for this type of series.
Now most people agree that while we have seen several ways of testing a series for convergence or divergence, knowing which test to use is always the hardest part. The key is to look for the form that fits the specifics of certain tests. And with that, let’s get ready to learn the last of our series test – the Root Test.
And I”m confident that you will agree that the Root Test is extremely helpful, and easy to use.
Root Test Video
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