Confusion on Summation Notation in Lagrange's Identity I'm working on a proof (the proof of Lagrange's Identity), but it includes a sum notation I'm not familiar with:
$$\sum_{1\le k\lt j\le n} (a_kb_j-a_jb_k)^2$$
I would appreciate any explanations of what this is saying, specifically in regards to the inequalities below the sigma.  Thanks!

For example, $1 \le k < j \le 5$ would indicate the $(j,k)$ pairs
\begin{array}{cccc}
   (2,1) \\
   (3,1) & (3,2) \\
   (4,1) & (4,2) & (4,3) \\
   (5,1) & (5,2) & (5,3) & (5,4)
\end{array}
