When doing an actuarial P&L, we always had to make use of the post: "difference with accountancy". That simply meant there were some results we couldnt explain, and if that post was not too big, the accountant didn't mind. A lot easier than writing a new website
I gave the Fraction class a try, adapting the class to the specifics of the assignment. Since the denominator is always of the form: 2^x, I only store x. I simplify where possible, and I hoped that that would be sufficient to keep the nominator as low as possible. Well, that did not work, for instance: if the series is 1/2 + 1/4 + 1/8 + .... then no term can be simplified. and so the numerator overflows after term 63 (if not earlier). So, the long nominator must be replaced by a BigInteger. I'll leave that to the real enthousiast (if any).
Here's the code: