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 a is a positive integer?
+876 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 a is a positive integer?
Using the geometric series formula, we have: 4/(1 - 5/a)
Simplifying we have: 4a/(a-5)
4a/(a-5) = k^2
4a = ak^2 - 5k^2
4a/k^2 = a-5
k^2 will always stay positive, so a-5 = 1 (least square)
a=6
