\mu(A)\leq\mu\bigcup_{n=1}^\infty(q_n-2^{-n-k},q_n+2^{-n-k})\leq\sum_{n=1}^\infty\mu((q_n-2^{-n-k},q_n+2^{-n-k}))=\sum_{n=1}^\infty 2^{-n-k+1}=\frac 1{2^{n-1}}