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Root Test

# Root Test - Root Test This is the last test for series...

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This is the last test for series convergence that we’re going to be looking at. As with the Ratio Test this test will also tell whether a series is absolutely convergent or not rather than simple convergence. Root Test Suppose that we have the series . Define, Then, 1. if the series is absolutely convergent (and hence convergent). 2. if the series is divergent. 3. if the series may be divergent, conditionally convergent, or absolutely convergent. A proof of this test is at the end of the section. As with the ratio test, if we get the root test will tell us nothing and we’ll need to use another test to determine the convergence of the series. Also note that if in the Ratio Test then the Root Test will also give . We will also need the following fact in some of these problems. Fact Let’s take a look at a couple of examples. Example 1 Determine if the following series is convergent or divergent. Solution

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Root Test - Root Test This is the last test for series...

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