An Interesting Series Sequel

In the infinite series 19+199++110n1+\dfrac{1}{9}+\dfrac{1}{99}+\cdots + \dfrac{1}{10^n-1}+\cdotsat what place after the decimal point does the second 11 occur?


Details and Assumptions\text{Details and Assumptions}

The first 11 occurs at the first place after the decimal point.

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