Let $\{T_n\}_{n\ge 1}$ be the sequence of numbers such that $T_1=5, S_n = \sum_{r=1}^n T_r$ . If $S_{m+n} –S_n –S_m=mn$, find $S_{100}$ and $T_{100}$.
I don't know how to proceed with the given information. I tried simplifying it but still got stuck. Please help me with it.