P = (1/2 + 3/8 + 5/32 + 7/128 + ...) / (1/2 + 1/8 + 1/32 + 1/128 + ...)
Let Q/2 be the numerator and S/2 be the denominator. Here is a visual solution:
And if you like calculus, here's an alternate way to calculate Q:
I guess now my blog will greet new readers with a wall of math for the next day or so.