The formula in focus is: (\sum_{j=k_1}^{k_2} score_f(s_j) + .. + \sum_{j=k_{t-1}}^{k_t} score_f(s_j) = t). The query seeks an elaboration or demonstration that could simplify the comprehension of how this formula operates or stands to be true from an intuitive standpoint. The request underscores a need for clarity on the mathematical representation and its application, indicating that while the formula appears logically sound, the practical visualization or conceptual grasp remains elusive.