In the first paragraph of Prove or Disprove this Darboux-like sum of a function defined on infinite limit points converges to zero, I state that I do not know whether this is a research question. Is this worthy of research? Do you know how to solve this problem?

Is my question clear? Can you visualize how to compute my sums for a give $n$? Do you know how to calculate $n^{\prime}$?