John Von Neumann and the Mathematician's Trap

From : John Von Neumann and the Mathematician’s Trap

The story goes that someone once posed to Von Neumann the following problem:

Two trains are 20 miles apart on the same track heading towards each other at 10
miles per hour, on a collision course. At the same time, a bee takes off from
the nose of one train at 20 miles per hour, towards the other train. As soon as
the bee reaches the other train, it bangs huwey and heads off at 20 miles per
hour back towards the first train. It continues to do this until the trains
collide, killing the bee.

The question is, how far does the bee fly (d) before the collision?

When posed with the above problem (or some variation of it), JVN took all of
five to ten seconds to come up with the correct solution. This floored the
questioner who said “I’m impressed that you didn’t fall for the Mathematician’s
Trap.” After getting a perplexed look from our genius, he asked “How did you
solve the problem?”

“By infinite series, of course!”