VWO 2007 Problem 1

The numbers $1,2, \ldots$ are placed in a triangle as following:

$\begin{matrix} 1 & & & 2 & 3 & & 4 & 5 & 6 & 7 & 8 & 9 & 10 \ldots \end{matrix}$

What is the sum of the numbers on the $n$ -th row?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.