|√2-√4|+|√4-√6|+|√6-√8|+······+|√2010-√2012|答案为|√2012-√2|

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/27 23:53:09
|√2-√4|+|√4-√6|+|√6-√8|+······+|√2010-√2012|答案为|√2012-√2|
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|√2-√4|+|√4-√6|+|√6-√8|+······+|√2010-√2012|答案为|√2012-√2|
|√2-√4|+|√4-√6|+|√6-√8|+······+|√2010-√2012|
答案为|√2012-√2|

|√2-√4|+|√4-√6|+|√6-√8|+······+|√2010-√2012|答案为|√2012-√2|
|√2-√4|+|√4-√6|+|√6-√8|+······+|√2010-√2012|
=√4-√2+√6-√4+√8-√6+...+√2012-√2010
=√2012-√2
=2√503-√2

绝对值里都是负的 都乘负-1 倒回来

√4-√2+√6-√4+√8-√6....+√2012-√2010
=-√2+(√4-√4)+(√6-√6)+(√8-√8)....+(√2010-√2010)+√2012
=√2012-√2

因为题干中每一个绝对值符号内都是后者大于前者,则可以打开绝对值如下:
|√2-√4|+|√4-√6|+|√6-√8|+······+|√2010-√2012|
= -√2+√4-√4+√6-√6+√8-······-√1998+√2010-√2010+√2012
=-√2+√2012
=|√2012-√2|