MathNet 1999 — Part 01 Question 159

For any finite set $S$, let $f(S)$ be the sum of the elements of $S$ (if $S$ is empty then $f(S)=0$). Find the sum over all subsets $E$ of $S$ of $\frac{f(E)}{f(S)}$ for $S=\{1,2, \ldots, 1999\}$.