At your own risk

Let $M_{n}= (0.a_{1}a_{2}a_{3} ... a_{n})$ where $a_{i} = 0 or 1, 1 \leq i \leq n-1 , a_{n}=1$ be a set of decimal fractions.

$T_{n} and S_{n}$ be the number and the sum of the elements in M, respectively. Then find $\lim_{n\to\infty} \frac {T_{n}}{S_{n}}$