=(1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)
=1+1+1+1+1+1+1-(1/2+1/4+1/8+1/16+1/32+1/64+1/128)
令a=1/2+1/4+1/8+1/16+1/32+1/64+1/128
则2a=1+1/2+1/4+1/8+1/16+1/32+1/64+1/64
所以a=2a-a=1/64-1
所以原式=7+1/64-1=6又1/64