Please help. I am rather stuck with this problem (and our lecturer says she doesn't know how to do this either). It is part of a proof that the Gamma function is holomorphic, but was omitted from the source material the lecturer used.
Let R > 1. Show that there is some M > 0 such that $| \frac {z^{2} − z}{2} - \frac{z^{3} − z}{3j} + \frac{z^{4} − z}{4j^{2}} - ... |≤ M$ for all z ∈ $\overline{B(0, R)}$ and every integer j > R.
$\overline{B(0, R)}$ denotes the closed ball of radius R centred at 0.
I tried writing the LHS term as a sum and was hoping to find a 'known' convergent sequence that would bound it, but haven't had any luck.