1/2+3/4+7/8+15/16+31/32+63/64+127/128
=1*64/128 + 3*32/128 + 7*16/128 + 15*8/128 + 31*4/128 + 63*2/128 + 127/128
=(64+69+112+120+124+126+127)/128
=752/128
=5.875