In the first quatrain I would walk

Then I would walk 500 miles for half of the

*additional*miles. In other words I would walk miles more, for a total of

Then I would walk 500 miles for a third of

*the last additional miles*(500 times 1/3 of the last term). In other words, miles more, for a total of

Continuing this pattern an infinite number of times, I would walk

For any value , the exact Maclaurin series expansion of is

Then, to put the number of miles I would walk into this form, we will factor out one of the 's. So

Then I would walk miles.

This distance is times larger than the lower bound for the estimated diameter of the universe.