Question 144
Let $M_n = \{0, a_1a_2\cdots a_n \mid a_i = 0 \text{or} 1, 1 \le i \le n-1, a_n = 1\}$ be a set of decimal fractions, $T_n$ and $S_n$ be the number and the sum of the elements in $M_n$ respectively. Then
$$
\lim_{n \to \infty} \frac{S_n}{T_n} = \underline{\hspace{2cm}}.
$$
$$
\lim_{n \to \infty} \frac{S_n}{T_n} = \underline{\hspace{2cm}}.
$$