Consider the geometric series 4 + 20/a + 100/a^2 + .... If the sum is a perfect square, what is the smallest possible value of a where is a positive integer?
The common ratio = 5/a
The sum = 4 / ( 1 -5/a) = (4) / [ ( a - 5) / a ] = (4a) / (a - 5)
The smallest integer value of a that produces a perfect square is when a = 9