Could anyone provide some hints for solving:

$\underset{n} {\mathrm{argmin}} \frac{a}{r + ns} + \sum_{i=0}^{n-1}\frac{b}{r + is}$ for $n \in \{1,2,3,\ldots\}$

The problem is part of a coding exercise, but I was curious whether an analytic solution could be derived.