计算:1/(1+√2)+1/(√2+√3)+1/(√3+√4)+…+1/(√8+√9)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/26 20:58:48
计算:1/(1+√2)+1/(√2+√3)+1/(√3+√4)+…+1/(√8+√9)
![](http://img.wesiedu.com/upload/1/ff/1ff4a45e9c0a972cfcb08d591da787dd.jpg)
![](http://img.wesiedu.com/upload/1/ff/1ff4a45e9c0a972cfcb08d591da787dd.jpg)
1/(1+√2)+1/(√2+√3)+1/(√3+√4)+1/(√4+√5)+···+1/(√8+√9)
=(√2-1)/(2-1)+(√3-√2)/(3-2)+(√4-√3)/(4-3)+···+(√9-√8)/(9-8)
=(√2-1)+(√3-√2)+(√4-√3)+(√5-√4)+···+(√9-√8)
=-1+√9
=-1+3
=2.
再问: 能解释一下为什么吗?
再答: 1/(1+√2)+1/(√2+√3)+1/(√3+√4)+1/(√4+√5)+···+1/(√8+√9)
=(√2-1)/(2-1)+(√3-√2)/(3-2)+(√4-√3)/(4-3)+···+(√9-√8)/(9-8)(把分母配成完全平方差,然后在同×﹣1))
=(√2-1)+(√3-√2)+(√4-√3)+(√5-√4)+···+(√9-√8)
=-1+√9
=-1+3
=2。
=(√2-1)/(2-1)+(√3-√2)/(3-2)+(√4-√3)/(4-3)+···+(√9-√8)/(9-8)
=(√2-1)+(√3-√2)+(√4-√3)+(√5-√4)+···+(√9-√8)
=-1+√9
=-1+3
=2.
再问: 能解释一下为什么吗?
再答: 1/(1+√2)+1/(√2+√3)+1/(√3+√4)+1/(√4+√5)+···+1/(√8+√9)
=(√2-1)/(2-1)+(√3-√2)/(3-2)+(√4-√3)/(4-3)+···+(√9-√8)/(9-8)(把分母配成完全平方差,然后在同×﹣1))
=(√2-1)+(√3-√2)+(√4-√3)+(√5-√4)+···+(√9-√8)
=-1+√9
=-1+3
=2。