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1/2+3/4+7/8+15/16+31/32+63/34+127/128+255/256+511/512+1023/1

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1/2+3/4+7/8+15/16+31/32+63/34+127/128+255/256+511/512+1023/1024
1/2+3/4+7/8+15/16+31/32+63/34+127/128+255/256+511/512+1023/1
1/2+3/4+7/8+15/16+31/32+63/34+127/128+255/256+511/512+1023/1024 =(1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)+(1-1/256)+(1-1/512)+(1-1/1024) =10-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/5121023/+1/1024) =10-1023/1024 =9又1/1024