Given that $$S=0.\dot{2}+0.\dot{0}\dot{3}+0.\dot{0}0\dot{4}+0.\dot{0}00\dot{5}+0.\dot{0}000\dot{6}$$, what is the sum of the first $2100$ digits of $S$ after the decimal point? 
Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals