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Unformatted text preview: ith exponentials:
Ratio Test or Root Test Using the ratio or root test, we know that the function will converge when the limit is less than 1, and will diverge when greater than 1. This will tell us all points (except at 2 points, called the endpoints, this happens when the limit is equal to 1, which means we must do another test) that will tell us where the series will converge! Since we only want to find the distance between these two points, we can find the radius by taking half of the distance. Strategy for Finding Radius of Convergence
Step 1: Determine which test (ratio or root) that you can use to test for convergence (note that you can use other tests as well, but most of the interesting/useful cases happen when we need to use ratio/root test).
Step 2: Solve for x based on the test that you are using (this will always give you an open bound when using the ratio or root test, as the limit can never equal 1).
Step 3: Half of the distance between the endpoints will be the radius. Example 1
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