Final answer:
The series is likely referring to a p-series in mathematics, which is convergent if k > 1. The other details provided seem to pertain to chemistry and are not relevant to the mathematical convergence of a series.
Step-by-step explanation:
The referring to the convergence of a mathematical series, but the singular use of 'k' and the references to equilibrium suggest that there may be a mix-up with chemistry content. In mathematics, a series converges for certain values of 'k' if the sum of its infinite terms approaches a finite limit.
Commonly, in the context of series, we talk about p-series, which have the form Σ 1/nk and are convergent if k > 1. This is a result of the p-series test for convergence. On the other hand, the references to equilibrium constants (K) and product/reactant concentrations seem to relate to chemistry, specifically to chemical equilibrium.
These do not have a direct bearing on the convergence of a mathematical series. Without the specific series in question or additional context, we can only infer based on standard mathematical convergence tests that for a p-series, the series is convergent for k > 1.