1/2+3/4+7/8+.+255/256
=（1-1/2)+(1-1/4)+(1-1/8)+(1+1/16)+...+(1/255/256)
=8-[(1/2)+(1/4)+...+(1/256)]
=8-[(1/2)+(1/4)+...+(1/256)]+(1/256-1/256)
=8-1+1/256
=7+1/256