At your own risk

Calculus Level pending

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 \[ \lim_{n\to\infty} \frac {T_{n}}{S_{n}} \]

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