Product of Summations

Theorem

 * $\ds \prod_{j \mathop = 1}^n \sum_{i \mathop = 1}^m a_{i j} = \sum_{1 \mathop \le i_1 \mathop, \mathop \ldots \mathop , i_n \mathop \le m} a_{i_1 1} \cdots a_{i_n n}$