1/2-(1/2-1/4)-(1/4-1/8)-.-(1/512-1/1024)

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1/2-(1/2-1/4)-(1/4-1/8)-.-(1/512-1/1024)
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1/2-(1/2-1/4)-(1/4-1/8)-.-(1/512-1/1024)
1/2-(1/2-1/4)-(1/4-1/8)-.-(1/512-1/1024)

1/2-(1/2-1/4)-(1/4-1/8)-.-(1/512-1/1024)
原式展开就是1/2-1/2+1/4-1/4+1/8-……-1/512+1/1024
两项相加都是0,最后就剩最后一项1/1024
所以结果是1/1024