1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256

1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256

1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
=(1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256 -1/256)+1/256
=(1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/128)+1/256
=...
=0+1/256
=1/256

1-1/2=1/2 ,1/2-1/4=1/4,依次这样算，所以最后减完就等于1/256.

1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256
原式=1-(1-1/2)+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+(1/16-1/32)+(1/32-1/64)+
(1/64-1/128) + (1/128-1/256)
=(1-1)+(1/2-1/2)+(1/4-1/4)+(1/8-1/8)+(1/16-1/16)+(1/32-1/32)+(1/64-1/64)+
(1/128-1/128)+1/256
=1/256

1-1/2=1/2
1-1/2-1/4=1/4
1-1/2-1/4-1/8=1/8
1-1/2-1/4-1/8-1/16=1/16
......
1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256-1/512=1/512