因为an=(5/9)×((10^n)-1))
所以sn=(5/9)×((10^1)-1))+(5/9)×((10^2-1))+…………+(5/9)×((10^n)-1))
=(5/9)×[(10^1+10^2+10^3+……+10^n)-n]
=(5/9)×[(10^(n+1)-10)/9-n]
=(5/81)×[(10^(n+1)-9n-10]
因为an=(5/9)×((10^n)-1))
所以sn=(5/9)×((10^1)-1))+(5/9)×((10^2-1))+…………+(5/9)×((10^n)-1))
=(5/9)×[(10^1+10^2+10^3+……+10^n)-n]
=(5/9)×[(10^(n+1)-10)/9-n]
=(5/81)×[(10^(n+1)-9n-10]