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How do I find the power series?

I know that

$\displaystyle\frac{1}{z+1} = \frac{1}{1-(-z)} = \sum_{n}^{\infty}(-z)^n$

and

$\displaystyle\frac{1}{(z+2)^2} = \frac{d}{dz} \frac{-1}{z+2} = \frac{d}{dz} \frac{-1}{1 - (-z-1)} = \sum_{n}^{\infty} -n(-z-1)^{n-1}$

But how do I do the above expression?