Taylor Expansion of complex function $ \frac{1}{1 - z - z^2} $ Knowing that 

$$c_{n+2}=c_{n+1}+c_n, \quad n \geq 0,$$ 

the problem is to prove that we have

$$ \frac{1}{1 - z - z^2}=\sum^{+\infty}_{n=0} c_nz^n.$$


I have tried to transform the function into the form:
$$ A(\frac{1}{z-b_1}+\frac{1}{b_2-z})$$
Then expand $\frac{1}{z-b_1} \text{and} \frac{1}{b_2-z}$
However, the result seems having nothing to do with $c_{n+2}=c_{n+1}+c_n$
Am I wrong? How should I prove this in a elegant way?

use this
$$\frac{8 x^2}{\sqrt{5} \left(\sqrt{5}+1\right)^2 \left(2 x+\sqrt{5}+1\right)}+\frac{8 x^2}{\sqrt{5} \left(\sqrt{5}-1\right)^2 \left(-2 x+\sqrt{5}-1\right)}+x+1$$
