Determine all nonnegative integers r such that it is possible for an infinite geometric sequence to contain exactly r terms that are integers. Prove your answer.

Assuming that you can choose the first term and the common ratio, it's possible for all positive integers.

S = F/ [1 - R], where S = sum of infinite series, F = First term, R = Common ratio

S = 4 / [1 - 6/7]

S = 4 / (1/7)

S = 4 x 7

S = 28 =7 + 6 + 5 + 4 + 3 + 2 + 1 + 0