[nhaehnle]

I'm not sure how you intended the example, but it's probably a bad one: If you take the integral of 1/x, say from x=1 to infty, you don't get a finite amount (because ln x goes to infinity).

On the other hand, if you take 1/x^2 as the integrand, you get the desired effect: its antiderivative is -1/x, so the integral of 1/x^2 from x=1 to infty is finite (actually, it's 1).

By the way: For good fun with convergent series, take a look at the problem of escaping a lion in a circular arena at equal maximum speeds. Here's an example link to both question and answer: http://puzzling.stackexchange.com/questions/8140/escaping-a-...

IIRC, there is an even more fascinating story associated to the history of this problem, as the first published solution was actually incorrect.

[jveld]

Thanks for the correction! It's been a couple years since I've actually done any calculus. I couldn't remember the exact function, so I had to google - I guess I read too quickly.