关于绝对值|1/21-1/20|+|1/22-1/21|+|1/23-1/22|+...|1/30-1/29|

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 13:20:16
关于绝对值|1/21-1/20|+|1/22-1/21|+|1/23-1/22|+...|1/30-1/29|

关于绝对值|1/21-1/20|+|1/22-1/21|+|1/23-1/22|+...|1/30-1/29|
关于绝对值|1/21-1/20|+|1/22-1/21|+|1/23-1/22|+...|1/30-1/29|

关于绝对值|1/21-1/20|+|1/22-1/21|+|1/23-1/22|+...|1/30-1/29|
=1/20-1/21+1/21-1/22+...+1/29-1/29+1/29-1/30
=1/20+(-1/21+1/21)+(-1/22+1/22)+.+(-1/29+1/29)-1/30
=1/20-1/30
=1/60

|1/21-1/20|+|1/22-1/21|+|1/23-1/22|+...|1/30-1/29|
=-1/21+1/20-1/22+1/21-1/23+1/22+...-1/30+1/29
=1/20-1/30
=1/60

1/60

这涉及到去绝对值。首先要判断绝对值符号里面的代数式的值的正负,正数直接去掉绝对值,负数等于其相反数。所以
|1/21-1/20|+|1/22-1/21|+|1/23-1/22|+...|1/30-1/29|
= -(1/21-1/20) - (1/22 - 1/21)-(1/23 - 1/22)-...-(1/30 - 1/29)
= -1/21+1/20-1/22+1/2...

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这涉及到去绝对值。首先要判断绝对值符号里面的代数式的值的正负,正数直接去掉绝对值,负数等于其相反数。所以
|1/21-1/20|+|1/22-1/21|+|1/23-1/22|+...|1/30-1/29|
= -(1/21-1/20) - (1/22 - 1/21)-(1/23 - 1/22)-...-(1/30 - 1/29)
= -1/21+1/20-1/22+1/21-1/23+1/22+...-1/30+1/29
=1/20-1/30
=1/60

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