Determine the coefficients of the power series I want to determine the coefficients $a_n$ of the power series $\Sigma_{n=0}^{\infty}a_nz^n=\frac{1}{(1-z)^2}$, where $|z|<1$ and $a_n,z \in \mathbb{C}$.
We have $\frac{1}{1-z}=\Sigma_{n=0}^{\infty}z^n$ and so $\frac{1}{(1-z)^2}=\Sigma_{n=0}^{\infty}\frac{z^n}{1-z}=\Sigma_{n=0}^{\infty}a_nz^n$. 
Therefore, $a_n=\frac{1}{1-z}$. Is this correct? 

No, because $a_n$ can't depend on $z$.
Try to compute the derivative of both sides of
$$
\frac1{1-x} = \sum_{n=0}^\infty x^n
$$instead.
