Source: C. Kosniowski's *Fun Mathematics on Your Microcomputer*, 1983, p. 17

**Hint:** Set up a table showing times, length of rubber band, and current position of snail. See a pattern?

**Solution Commentary:** By setting up the table, you should see that at the time of N minutes, the snail has crawled N inches and the length of the rubber band is 7N inches.

The relative position of the snail to the rubber band's length is 1/7 + 1/14 + 1/21 + ... + 1/7N after N minutes.

This can be factored to produce (1/7)(1 + 1/2 + 1/3 + ... + 1/N), suggesting the Harmonic Series is involved....which is divergent and we thus know the relative position of the snail eventually exceeds 1.

That is, when N is about e^{7}/(1.781) the series expression is 7/7, or the snail reaches the end of the rubber band!

At this stage, the time N required is slightly less than 10 1/4 hours.

Now, if the rubber band had been 10 inches long at the start, the snail would need more than 8 days to reach the end.

If the rubber band had been 100,000 inches long (slightly longer than 1.5 miles) at the start, the snail would reach the end....but would need a time length greater than the estimated age of the universe....so is it possible?

Ah, the power of the Harmonic Series strikes again!