PIMSO 2022 - Mathematics - Grade 9 / Secondary 3 - National Round Question 15

Simplify $S=\frac1{10}+\frac2{10^2}+\frac3{10^3}+\frac4{10^4}+\frac5{10^5}+\frac6{10^6}+\frac7{10^7}+\frac8{10^8}+\frac9{10^9}$.