Consider the geometric series \(4+\frac{12}{a}+\frac{36}{a^2}+\cdots\). If the sum is a perfect square, what is the smallest possible value of a where a is a positive integer?
Formula: Sum = (first term) / [ 1 - (common ratio) ]
For this series, the common ratio is 3/a
---> Sum = 4 / [ 1 - 3/a ] ---> Sum = (4a) / (a - 3)
---> 4 is the smallest value for a to result in a perfect square
+981 
