# How do you find a power series representation for # x^2 / ( 1 - 2x )^2#?

The idea is to relate this expression to the known power series expansion

Quick substitution:

Let's find the power series representation for the differentiated expression:

So,

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To find the power series representation for ( \frac{x^2}{(1 - 2x)^2} ), you can start by expressing ( \frac{1}{(1 - 2x)^2} ) as a power series. This can be done using the geometric series formula. Then, you can differentiate this series term by term and multiply by ( x^2 ) to get the desired series representation.

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