An other alternative that may be easier to do in the head is to split out 50 and 100, and do 1+99, 2+98, ... 49+51. 49*100 + 50 + 100. By the way, it was Karl Friedrich Gauss who was the student.

Things tends to be easy when you know the solution. The hard thing is to quickly see the existence of multiple solutions (or even one) to new problems you haven't seen before.

This is also a bit in line with one of Arthur C. Clarkes three laws: "Any sufficiently advanced technology is indistinguishable from magic." Without knowing how to solve infinite series, the von Neumann feat will seem impossible.