Determing the Mclaurin series of $\frac{z^2}{(1+z)^2}$

Question

Determine the Mclaurin series and the radius of convergence for the function:

$$\frac{z^2}{(1+z)^2}$$

I guess I am supposed to adapt the following series $\frac{1}{1+z}=\sum_\limits{n=0}^{\infty}(-1)^n z^n,\:|z|<1$

$\frac{z^2}{(1+z)^2}=z^2.\frac{1}{(1+z)^2}$

I cannot get past the last step.

Question:

How should I solve the problem?

Thanks in advance!

Answer 1

Hint: Differentiate the series you listed.