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 is 5/a
The sum is
4 4a
_______ = _____
1 - 5/a a - 5
Note that when a = 9
4(9) 36
____ = _______ = 9 = perfect square
9 - 5 4
