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

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/24 17:12:41
计算|1/3-1/2|+|1/4-1/3|+|1/4-1/3|+|1/5-1/4|+.+|1/20-1/19|
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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|
计算|1/3-1/2|+|1/4-1/3|+|1/4-1/3|+|1/5-1/4|+.+|1/20-1/19|

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

展开=1/2-1/3+1/3-1/4+1/4……+1/19-1/20=1/2-1/20=9/20具体点因为1/3-1/2=-1/6, 所以|1/3-1/2|=1/6=1/2-1/3, 同理该式子的每项绝对值展开后都等于后一个数字减去前一个数字, 即|1/3-1/2|=1/2-1/3,|1/4-1/3|=1/3-1/4, 然后就是展开=1/2-1/3+1/3-1/4+1/4……+1/19-1...

全部展开

展开=1/2-1/3+1/3-1/4+1/4……+1/19-1/20=1/2-1/20=9/20

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