解：原式=1-1/2+1-1/4+1-1/8+1-1/16+1-1/32+1-1/64+1-1/128+1-1/256
=8-（1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256）
期中1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+（1/256+1/256）-1/256
=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128-1/256
……
=1-1/256
所以原式=8-（1-1/256）=7+1/256
(1-1/2)+(1-1/4)+(1-1/8)+ +(1-1/256)=
8-(1/2+1/4+ +(1/2)^8)=8－(1-1/256)=7＋1／256
7又256分之1
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