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

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://tutor.hix.ai

The convergence interval in

The attached figure shows the agreement between

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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