$ (1+2+3+4+\cdots)\cdot\left(\begin{array} {} & \text{one} \\[6pt] + & \text{two} \\[6pt] + & \text{three} \\[6pt] + & \text{four} \\[6pt] + & \cdots \end{array}\right) $ $ = \sum \left[ \begin{array}{cccc} 1\cdot\text{one}, & 2\cdot\text{one}, & 3\cdot\text{one}, & 4\cdot\text{one}, & \cdots\\[6pt] 1\cdot\text{two}, & 2\cdot\text{two}, & 3\cdot\text{two}, & 4\cdot\text{two}, & \cdots\\[6pt] 1\cdot\text{three}, & 2\cdot\text{three}, & 3\cdot\text{three}, & 4\cdot\text{three}, & \cdots\\[6pt] 1\cdot\text{four}, & 2\cdot\text{four}, & 3\cdot\text{four}, & 4\cdot\text{four}, & \cdots\\ \vdots & \vdots & \vdots & \vdots & \ddots \end{array} \right] $ \begin{align} & = \cdots\cdots\cdots +\sum\left[ \begin{array}{cccc} \cdot & \cdot & 3\cdot\text{one}, & \cdot & \cdots\\[6pt] \cdot & 2\cdot\text{two}, & \cdot & \cdot & \cdots\\[6pt] 1\cdot\text{three}, & \cdot & \cdot & \cdot & \cdots\\[6pt] \cdot & \cdot & \cdot & \cdot & \cdots\\ \vdots & \vdots & \vdots & \vdots & \ddots \end{array} \right] \\[18pt] & {}\qquad\qquad\qquad{}+ \sum\left[ \begin{array}{cccc} \cdot & \cdot & \cdot & 4\cdot\text{one}, & \cdots\\[6pt] \cdot & \cdot & 3\cdot\text{two}, & \cdot & \cdots\\[6pt] \cdot & 2\cdot\text{three}, & \cdot & \cdot & \cdots\\[6pt] 1\cdot\text{four}, & \cdot & \cdot & \cdot & \cdots\\ \vdots & \vdots & \vdots & \vdots & \ddots \end{array} \right] + \cdots\cdots\cdots \end{align}