Find the function represented by a power series

 Objective: Find the function represented by a power series

In the previous post, a function was given. The task was to find the corresponding power series. In this post we do the inverse problem. A power series is given. We need to find the corresponding function

Example

Solution

This is a geometric series that is convergent only and only if ❘2x❘<1 i.e -1<2x<1

-1/2<x<1/2. The series is convergent in the interval (-1/2, 1/2)

Practice