I'm reading "How would you move Mount Fuji?", and one of the puzzzles/questions is:
A train leaves Los Angeles for New York at a constant speed of 15 miles an hour. At the same moment, a train leaves New York for Los Angeles on the same track. It travels at a constant 20 miles an hour. At still the same moment, a bird leaves the Los Angeles train station and flies toward New York, following the track, at a speed of 25 miles an hour. When it reaches the train from New York, it instantly reverses direction. It travels at the same speed until it reaches the train from Los Angeles, when it reverses again, and so forth. The bird flies back and forth between the two trains until the very moment they collide. How far will the bird have travelled?
In the answer, they mention that it could be solved by using an infinite series (and that most people will probably have forgotten how to do it when asked in an interview, and that John von Neumann did so almost instantly when asked this type of question), but they do it another way. First, they note that the time until the trains crash is given by h, and d = 15h + 20h, where d is the distance (they use 3500). Thus, h = 100 hours. The distance that the bird travels is 25d. Thus, the answer is 2500 miles.
I'm curious though, how does one solve this using an (infinite) series? How does one write this problem as a series in the first place? The only thing that I can get is that the series (of the hours that the bird spends flying) starts like this: (77.77, 9.73, ...)