The Curious Behavior of 1/7 (Proposed Problem)

Problem. A curious property of 1/7 is that to two decimal places it equals 2 x 7 percent, that is .02 x 7. Add .o2 sup 2 x 7 and you obtain 1/7 to four decimal places. Add .02 sup 3 x 7 and you obtain it to six places (with an error of 1 in the last place), and so on. In fact 1/7 equals 7 times the sum of a pure geometric series whose ratio has a terminating decimal expansion.