Consider the following section in a proof in my notes:
We show here that, as a consequence of Cauchy's integral formula any holomorphic function g(z) in an open domain D is analytic. Consider a circle centered on $z_0$, within D, and a point z inside the circle. One can write
$$g(z) = \frac{1}{2i\pi} \oint_C dz' \frac{g(z')}{z'-z} = \frac{1}{2i\pi} \oint dz' \frac{g(z')}{(z'-z_0) - (z-z_0)}$$
and since $|z-z_0| < |z'-z_0| $ one can expand the integrand as
$$g(z) = \frac{1}{2i\pi} \oint dz' \frac{g(z')}{z'-z_0} \sum_{n=0}^{\infty}\bigg(\frac{z-z_o}{z' -z_o} \bigg)^n$$
My question is how do we get frost the first line to the second line I am unsure where the summation came from.