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1/2+3/4+7/8+15/16+31/32+······+511/512+1023/1024简便计算
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答案和解析
1024=2^10,所以有十个式子,所以
原式= 10-(1/2+1/4+1/8+.+1/1024)
=10-(1/2+1/4.+1/1024+1/1024-1/1024)
= 10-(1/2+1/4.+1/512+1/512-1/1024)
=10-(1-1/1024)
=9+1/1024
原式= 10-(1/2+1/4+1/8+.+1/1024)
=10-(1/2+1/4.+1/1024+1/1024-1/1024)
= 10-(1/2+1/4.+1/512+1/512-1/1024)
=10-(1-1/1024)
=9+1/1024
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