What is the appropriate mathematical notation to describe the folowing relationship ?
$$ S = \frac{N_{1}}{T_{1}} + \frac{N_{1} + N_{2}}{T_{2}} + \frac{N_{1} + N_{2} + N_{3}}{T_{3}} + \cdots +\frac{N_{1} + N_{2} + \cdots + N_{k}}{T_{k}} $$
Is it as follows ? $$ S = \sum_{i=1}^{k}\frac{\sum_{i=1}^{i}N_{i}}{T_{i}} $$