# Converting complex power series into a function

 Sci Advisor HW Helper P: 4,300 I'd probably start with something like $$\sum_{n = 0}^\infty z^n = \frac{1}{1 - z}$$ for |z| < 1, and look at its derivatives to get the factors of n in front. E.g. $$\frac{d^2}{dx^2} \sum_{n = 0}^\infty z^n = \sum_{n = 0}^\infty n^2 z^{n - 2} + \frac{1}{z} \sum_{n = 0}^\infty n z^{n - 1}$$ and then do a bit of shifting and some more magic with the first derivative.