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计算|1/3-1/2|+|1/4-1/3|+|1/4-1/3|+|1/5-1/4|+.+|1/20-1/19|

来源:学生作业帮 编辑:拍题作业网作业帮 分类:数学作业 时间:2024/04/30 14:30:49
计算|1/3-1/2|+|1/4-1/3|+|1/4-1/3|+|1/5-1/4|+.+|1/20-1/19|
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/20-1/19|
=1/2-1/3+1/3-1/4+1/4-1/5+.+1/19-1/20
=1/2-1/20
=9/20
再问: 这是两个|1/4-1/3|
再答: |1/3-1/2|+|1/4-1/3|+|1/4-1/3|+|1/5-1/4|+......+|1/20-1/19| =1/2-1/3+1/3-1/4+1/3-1/4+1/4-1/5+......+1/19-1/20 =1/2+1/3-1/4-1/20 =30/60+20/60-15/60-3/60 =8/15