Question 1
For $-1 \lt r \lt 1,$ let $S(r)$ denote the sum of the geometric series $$
12 + 12r + 12r^2 + 12r^3 + \cdots.
$$ Let $a$ between $-1$ and $1$ satisfy $S(a)S(-a) = 2016.$ Find $S(a) + S(-a).$
12 + 12r + 12r^2 + 12r^3 + \cdots.
$$ Let $a$ between $-1$ and $1$ satisfy $S(a)S(-a) = 2016.$ Find $S(a) + S(-a).$