1-1/10-1/100-1/1000-.-1/100000000=?简便计算过程

=0.8888 8889
因为
1=0.9999 9999 + 0.0000 0001，也就是拆成两部分
然后用它去分别减 1/10 1/100 1/1000-......-1/100000000
你会发现就是把0.9999 9999 各个数位上的9减1，得到0.8888 8888
最后再加上拆出来的0.0000 0001，把它加回去，就是0.8888 8889

设A=1-1/10-1/100-1/1000-......-1/100000000
10A=10-1-1/10-1/100-……-1/10000000
10A-A=(10-1-1/10-1/100-……-1/10000000)-(1-1/10-1/100-1/1000-......-1/100000000)
9A=9-1/100000000
A=1-1/900000000
A=899999999/900000000
1-1/10-1/100-1/1000-......-1/100000000=899999999/900000000

1-1/10-1/100-1/1000-......-1/100000000=1-(1/10+1/100+1/1000+......+1/100000000)=1-(1-0.1^8)/(1-0.1)=-0.9999999988888888889(八循环)

1-1/10-1/100-1/1000-......-1/100000000=1-11111111/100000000=88888889/100000000

1-1/10-1/100-1/1000-.-1/100000000
=1-0.1-0.01-0.001-0.0001-……-0.00000001
=1-（0.1+0.01+0.001+0.0001+……+0.00000001）
=1-0.11111111
=0.88888889