Question

Why does the end point change when we take the integral or derivative of a power series?

Answer 1

Let the power series converge on the interval, Then it is differentiable on the same interval.h

It can be noted that if a power series is differentiated , then the differentiated series has the same interval of convergence as the original series except possibly the loss of one or both end points of the interval of convergence if the original series was convergent at these points.

If a power series is integrated, then the series has the same interval of convergence as the original series except ossibly the gain of one or both end points of the interval of convergence if the original series wasnt convergent at the end points already.