Refer to the application at the beginning of the lesson. What type of interference results? Explain.
Example 1 Determine the radius of convergence and interval of convergence for the following power series. Solution Okay, we know that this power series will converge for , but that’s it at this point. To determine the remainder of the x’s for which we’ll get convergence we can use any of the tests that we’ve discussed to this point. After application of the test that we choose to work with we will arrive at condition(s) on x that we can use to determine which values of x for which the power series will converge and which values of x for which the power series will diverge. From this we can get the radius of convergence and most of the interval of convergence (with the possible exception of the endpoints).