The answer is not what it seems

In the infinite series

\[ \frac { 1 }{ 9 } +\frac { 1 }{ 99 } +......+\cfrac { 1 }{ { 10 }^{ n }-1 } + \ldots \]

at what place after the decimal point does the third 1 occur?

Note: The first 1 occurs at the first place after the decimal point.


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