General Distributivity Theorem/Examples/Sum of j from m to n by Sum of k from r to s

Example of General Distributivity Theorem

 * $\displaystyle \sum_{j \mathop = m}^n \sum_{k \mathop = r}^s j k = \frac 1 4 \left({n \left({n + 1}\right) - \left({m - 1}\right) m}\right) \left({s \left({s + 1}\right) - \left({r - 1}\right) r}\right)$

for $m \le n, r \le s$.