# complex analysis – find Taylor's series but the center is not analytic

I want to find a Taylor series for the complex function

$$f (z) = dfrac {z ^ 2} {2 + z},$$ focused on $$z = 2$$.

I've found the taylor series $$f (z)$$ focused on $$z = z_0$$,
$$f (z) = (z-2) + dfrac {4} {z + 2} = (z-2) +4 sum limits_ {n = 0} ^ infty dfrac {(- 1) ^ n} {(2 + z_0) ^ {n + 1}} (z-z_0) n.$$

Since $$f (z)$$ is not analytic to $$z = 2$$, can we find Taylor's series?