smc

We can represent the bug's position on the coordinate plane using complex numbers. The first move the bug makes is $1$, the second $i/2$, the third $-1/4$, and so on. It becomes clear that the distance the bug travels is an infinite geometric series with initial term 1, and common ratio $i/2$. Thus, applying the infinite geometric series formula: $\frac{1}{1-\frac{i}{2}}=\frac{1}{\frac{2-i}{2}}=\frac{2}{2-i}=\frac{2(2+i)}{(2-i)(2+i)}=\frac{4+2i}{5}$ This is equivalent to the $x$ coordinate being $4/5$ and the $y$ coordinate being $2/5$, so the answer is $\boxed{(\frac{4}{5},\frac{2}{5})}$