Understanding Taylor Series for Solving Complex Equations

[xspook]

Homework Statement

f(x)=\frac{4x}{(4+x^{2})^{2}}

Homework Equations

\frac{1}{1-x} = \sum x^{n}

The Attempt at a Solution

How am I supposed to use that equation to solve the main problem. I have the solution but I don't understand how to do any of it. My professor is horrible, been on academic probation for 7 years, and doesn't teach us anything. Just writes on the board

 

[xspook]

Sorry I meant to say MacLaurin series. A friend told me I have to solve it using infinite series but that still has me confused

 

[STEMucator]

Wait... what is the problem exactly?

 

[SammyS]

Homework Statement

f(x)=\frac{4x}{(4+x^{2})^{2}}

Homework Equations

\frac{1}{1-x} = \sum x^{n}

The Attempt at a Solution

How am I supposed to use that equation to solve the main problem. I have the solution but I don't understand how to do any of it. My professor is horrible, been on academic probation for 7 years, and doesn't teach us anything. Just writes on the board

Please state the problem word for word as it was given to you. We can guess what you're supposed to find but ...