# How do you find a power series representation for #1/(1-x)^2 # and what is the radius of convergence?

##### 1 Answer

#### Explanation:

We are given

This is fairly similar to

The radius of convergence for this power series is

While it would be easy to say that

This is not a valid representation of a power series.

Usually, some power series arise from **derivatives**. It'd be worth a shot to try this one, too.

By the quotient rule,

As

Hence the power series representation of

with radius of convergence