1/2=1-1/2
1/4=1/2-1/4
1/8=1/4-1/8
1/16=1/8-1/16
1/2+1/4+1/8+1/16
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)
=1-1/16
=15/16