Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.

Solution 15EStep 1:In this problem we have to determine the radius of convergence of the power series.Use Ratio test to determine the radius of convergence.If and1. If L <1, converges.2. If L >1, diverges.3. If L=1, the test is inconclusive.Step 2: Consider ,= = | | = | | = | | = | |(1) = | |Step 3:The series converges for L<1.Therefore solve By using “If ”-< x < Thus the radius of convergence is .