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