# Thread: Power series representation of a function

1. ## Power series representation of a function

$f(x) = \frac{x^3}{(x-11)^2}$

On ones like this I usually just start with $\frac{1}{1-x}$ & differentiate and then multiply and divide terms back in to get my final power series, but with the $~x^3~$on top, how should I work this? I thought about just factoring out one of the x's on top and setting it outside the series, can I do that?

2. ## yes

find your powere series for 1/(x-1)^2 and multiply each term in the result by x^3 so for example a term of the form x^k becomes x^(k+3)