I had to make a bunch of band limited digital triangle waves recently, so I went to (where else) wikipedia for the equations.

I noticed that there is a constant amplitude scalar of `8/pi^2` (`~.8106`). And indeed this does bring the amplitude range down to about +/-1. The wikipedia article (https://en.wikipedia.org/wiki/Triangle_wave#Harmonics) doesn't explain the theoretical reasoning for this but I would like to know why this is so.