0.818181........+0.323232........-0.585858........=?

0.818181........+0.323232........-0.585858........
=(0.81+0.32-0.58)*(1+0.01+0.0001+0.000001......)
=0.55*(1+0.01+0.0001+0.000001......)
=0.55+0.0055+0.000055+0.00000055......
=0.5555555555555......

0.81818181……=0.81+0.0081+0.000081+……相当于首项为0.81，公比为0.01的等比数列的无穷多项和，由无穷多项和的公式
S=a1/(1-q)=0.81/(1-0.01)=81/99
同理0.323232……=32/99
0.585858……=58/99
于是原式等于=81/99+32/99-58/99=55/99=5/9=0.55555555……

把小数化分数：
0.818181....=81/99=9/11
0.323232....=32/99
0.585858....=58/99
所以：原式=（81+32-58）/99=5/9

1.7272727272.................