In article <32FA8404.5DD6@geocities.com>, Luka Crnkovic <email@example.com> wrote: >Everybody has heard the problem: > >Two trains 200 miles apart are moving toward each other; >each one is going at a speed of 50 miles per hour. > A fly starting on the front of one of them flies back and forth >between them at a rate of 75 miles per hour. It does this until the >trains collide and crush the fly to death. What is the total distance >the fly has flown? > >The solution is simple, using s=t*v, but is ther another way >of solving it by trough limit?
If you notice the whole thing lasts 2 hours, you see at once the answer is 150 miles. But you might instead work out that the first leg of the fly's trip lasts 1.6 hours and is 120 miles long; the second leg is 1/5 as long, 24 miles; the third, likewise, is 4.8 miles; and so on. You sum the infinite series (a geometric one)... and get 150 miles, the hard way.
The story goes, someone gave this to von Neumann and the latter gave the answer in a few seconds. -- "Ah, of course you saw the quick method... You know, some people try to sum the infinite series..." -- "What do you mean?... I _did_ sum the infinite series..."