Consider the set of all fractions of the form $\frac{2^m}{3^n},$ where $m$ and $n$ are integers such that $0 \le m \le n.$ For example, 1/9 and 8/27 would be included in this set, but not 32/81. What is the sum of all the numbers in this set?
The answer is (B) 27/16.