- #1

aerospacev

- 4

- 0

## Homework Statement

Find a power series representation for the function [itex] f(x) = \frac{(x-1)}{(3-x)^2}^2[/itex], valid for every [itex]x[/itex] with [itex]|x|<3[/itex]

## Homework Equations

The equation that I think would be useful is [itex]\frac{1}{1-x} = \sum_{n=0}^\infty x^n[/itex]

## The Attempt at a Solution

I began by just looking at the term [itex]\frac{1}{(3-x)^2}[/itex]

[itex]\frac{1}{1-x} = \sum_{n=0}^\infty x^n[/itex]

differentiating both sides:

[itex]\frac{1}{(1-x)^2}= \sum_{n=1}^\infty nx^{(n-1)}[/itex]

now I'm stuck here, my train of thought is that if I can turn [itex]\frac{1}{(3-x)^2}[/itex] into someform of [itex]\frac{1}{(1-x)^2}[/itex] to obtain its summation formula, I can then multiply the polynomial [itex]{(x-1)}^2[/itex] to that summation and go from there.

Usually the assignment questions involve functions in the likes of [itex]\frac{x}{(1-x^2)}[/itex] or [itex]\frac{x^2}{(1+x)^3}[/itex], which I can solve, but the [itex] 3 [/itex] in front of the x in [itex]\frac{1}{(3-x)^2}[/itex] is really troubling me, any help? Thanks!