# Finding the Maclaurin series representation

1. Apr 15, 2013

### Turion

Edit: Never mind. Got it.

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

I tried finding the first derivative, the second derivative, and so on, but it just keeps getting more complicated, so I suspect I have to use binomial series.

The issue is that binomial series needs to have the form of ${ (1+x) }^{ k }$ but I can't get it into that form. Any idea to get f(x) into that form? The x outside won't go inside the brackets.

Here is the theorem: http://s9.postimg.org/u4qwkrmv3/Binomial_Series.png [Broken]

Also, my textbook has only one example on binomial series and it is a simpler example.

Attempt:

$$f(x)=\frac { x }{ { (2-x) }^{ 2 } } \\ f(x)=\frac { x }{ 4{ (1-\frac { x }{ 2 } ) }^{ 2 } } \\ f(x)=\frac { 1 }{ 4{ x }^{ -1 }{ (1-\frac { x }{ 2 } ) }^{ 2 } }$$

Last edited by a moderator: May 6, 2017
2. Apr 15, 2013

### LCKurtz

Leave the $x/4$ out in front and expand$$\left (1-\frac x 2\right)^{-2}$$then multiply the $x/4$ back in the result.

 Apparently you got it while I was typing this.