# Power series representation of a function

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• April 12th 2009, 01:06 PM
mollymcf2009
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?
• April 12th 2009, 01:35 PM
Calculus26
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)