Harmonic series (mathematics)
A swimmer that goes faster each time they touch the wall of the pool. The swimmer starts crossing a 10-meter pool at a speed of 2 m/s, and with every crossing, another 2 m/s is added to the speed. In theory, the swimmer's speed is unlimited, but the number of pool crosses needed to get to that speed becomes very large; for instance, to get to the speed of light (ignoring special relativity), the swimmer needs to cross the pool 150 million times. Contrary to this large number, the time needed to reach a given speed depends on the sum of the series at any given number of pool crosses: