Don't forget to carry

If the following infinite series SS is evaluated as a decimal,what is the 37th digit to the right of the decimal place?

S=19+199+1999++110n1+ \large S=\frac { 1 }{ 9 } +\frac { 1 }{ 99 } +\frac { 1 }{ 999 } +\ldots + \frac { 1 }{ { 10 }^{ n }-1 } + \ldots

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