Series rapresentation $f(t)=\frac{1}{(2t+1)^{2}}$ How to find the series rapresentation in $t=0$ of the following expression
$$f(t)=\frac{1}{(2t+1)^{2}}$$
Can someone show me also the steps.
Thank you so much!

$\displaystyle \frac{1}{1-x}=\sum\limits_{n=0}^\infty x^n\enspace$ for $\enspace-1<x<1$ , proof by multiplication with $1-x$ . 
One derivation for $x$ gives $\enspace\displaystyle \frac{1}{(1-x)^2}=\sum\limits_{n=1}^\infty nx^{n-1}$ . 
With $x:=-2t$ and therefore $\enspace -\frac{1}{2}< t< \frac{1}{2}$ follows:
$$\displaystyle \frac{1}{(1+2t)^2}=\sum\limits_{n=1}^\infty n(-2t)^{n-1}$$ 
