计算:|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+······+|1/20-1/19|

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/16 10:39:43
计算:|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+······+|1/20-1/19|

计算:|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+······+|1/20-1/19|
计算:|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+······+|1/20-1/19|

计算:|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+······+|1/20-1/19|
|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+······+|1/20-1/19|
=1/3-1/4+1/4-1/5+1/5-1/6+...+1/19-1/20
=1/3-1/20
=20/60-3/60
=17/60

|1/4-1/3|+|1/5-1/4|+|1/6-1/5|+······+|1/20-1/19|=1/3-1/4+1/4-1/5+1/5-1/6+······+1/19-1/20=1/3-1/20=17/60

1/4<1/3 ...............
原式=-(1/4-1/3+1/5-1/4+...+1/20-1/19)
=-[1/20-1/3+(1/4-1/4+1/5-1/5+...+1/19-1/19)]
=-(1/20-1/3)
=20/60-3/60
=17/60

因为每一项绝对值符号里的算式都是负数,所以等于加上他的负数。所以原算式=1/3-1/4+1/4-1/5+1/5-1/6+······+1/19-1/20=1/3-1/20=17/60