I am trying to find the interval of convergence for the attached power series (attached as a gif). I am also supposed to check the endpoints for convergence. I'm not that good with power series and the format of this power series is really throwing me off. So I am looking for the steps to find the interval of convergence (also checking the end points).© BrainMass Inc. brainmass.com February 24, 2021, 2:10 pm ad1c9bdddf
An automatic response to a power series of this type is to use the ratio test. In the ratio test, you want to look at the limit as n goes to infinity of the absolute value of a_n+1 / a_n:
This provides the steps to find the interval of convergence (also checking the end points).