You can also prove it a different way if you allow the use of the formula for finding the limit of the sum of a geometric series on a non-convergent series.
Open Hexagon is pretty good if you enjoy music reaction/arcade games. It’s an open source successor of Super Hexagon with several community made level packs. The only flaw is the steep learning curve of the gameplay.
Bit hacker 2 is really fascinating. It uses a bit mask of all 1s (-1) or all 0s (0) and takes advantage of the fact that y ^ (x ^ y) = x and y ^ 0 = y