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