Use geometric series to express `0. 555... =0. overline5` as`\ ` a rational number

Explanation

Expansion of `0. 555...`


`=0.5+0.05+0.005+0.0005+...`


`=5[10^(-1)+10^(-2)+10^(-3)+10^(-4)+10^(-5)+10^(-6)+...]`


It is infinite geometric series


`a=10^(-1), r=10^(-1)`


`S=a/(1-r)`


`S=5*0.1/(1-0.1)`


`S=5*0.1/(0.9)`


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