Question

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Answer 1

Figure out how long the train takes to reach B. Multiply that time by the pigeon's speed to get the distance the pigeon flew. Or, if channeling John von Neumann, add up the sum :-)

Answer 2

That's right, it doesn't account for them, because it isn't necessary to do so to solve the problem.

Answer 3

The pigeon is flying continuously for the time that it takes the train to go from A to B. You know that time (or can find it), and you know the pigeon's speed. That's all you need to find the distance flown by the pigeon.

Answer 4

As the train approaches B, the distance flown by the pigeon gets SMALLER, because it is flying from B->train->B->train etc.

Answer 5

And the train does arrive, the problem statement says so. And you can add up the infinite series of ever smaller terms, just like the sum in Xeno's paradox converges.

Answer 6

For what it's worth, I know a guy named Xeno, and he never has any trouble getting places :-)

Answer 7

I'm not sure what the "polymath way" is...

Answer 8

where did you learn it?