2分之1加4分之1加8分之1加16分之1加64分之1加128分之1加256分之1 等于几？ 过程也写出来。

法① 1/2=1-1/2
1/4=1/2-1/4
1/2+1/4=1-1/2+1/2-1/4=1-1/4=3/4
…………
则推导可得1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=1-1/256=255/256
法② 设s=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
则2*s=1+1/2+1/4+1/8+1/16+1/32+1/64+1/128
s=2*s-s=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
=1-1/256=255/256

256分之255

1/2+1/4+1/8+1/16+1/64+1/128+1/256
=(1/2+1/4)+(1/8+1/16)+(1/64+1/128)+1/256
=(2/4+1/4)+(2/16+1/16)+(2/128+1/128)+1/256
=3/4+3/16+3/128+1/256
=(3/4+3/16)+(3/128+1/256)
=(12/16+3/16)+(6/256+1/256)
=15/16+7/256
=240/256+7/256
=247/256

100000