# How do you find a power series representation for #(x-2)^n/(n^2) # and what is the radius of convergence?

##### 1 Answer

#### Explanation:

Suppose that our quest is for

In this case a variable change

In the next steps we will try to build such a power series.

We begin with

This power series is convergent for

now integrating

The last step is covered by integrating

or equivalently

The description of function PolyLog can be found in

https://en.wikipedia.org/wiki/Polylogarithm

The convergence interval in

The attached figure shows the agreement between