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.