I Would Walk Five Hundred Miles (Part 2)

Pleased with his self-assessed cleverness, Robert thinks to himself, "She must be so impressed. ...There's no way Derek can best that."

But, while slightly surprised by Robert's attempt to woo the woman of both their affections, Derek remains, nevertheless, unscathed. Eyes fixed on his love, Derek steps up to the microphone for his turn.

Well I would walk EIGHT hundred miles
And I would walk eight hundred more
For each of those eight hundred miles
That I said I would walk before

Then I would walk 799 miles
For half of those additional miles
Then I would walk 798 miles
For a third of those additional miles

Then I would walk 797 miles
For a fourth of those additional miles
And so on and so forth
Until I would walk 0 additional miles

Da da da da
Da da da da
Da da da da
Da da da da

Robert busts out laughing. "Eight hundred?! HAHAHAHAHA! He picked a bigger number and then decreases to zero while I multiply by five hundred an infinite number of times! What an idiot!"

...or is he? Who's the real idiot here? Find how far Derek would walk.

Then, supposing that he who would walk farther gets the girl, which one gets the girl?

(Solution)