As he played with his series, he noticed that in some of them each step in the calculation added a smaller and smaller amount to the total. Extending the operation by hand—row after row of numbers, a strangely beautiful triangle, growing across the page—produced a better and better fit to the ultimate answer. The endpoint, well beyond the stamina of even so heroic a numbers-cruncher as Newton, was obvious: the last terms in such series must dwindle toward nothing.
