1/(√3+1)+1/(√5+√3)+1/(√7+√5)+.+1/√2n+1+√2n+1怎么化简

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 04:01:06

1/(√3+1)+1/(√5+√3)+1/(√7+√5)+.+1/√2n+1+√2n+1怎么化简
1/(√3+1)+1/(√5+√3)+1/(√7+√5)+.+1/√2n+1+√2n+1怎么化简

1/(√3+1)+1/(√5+√3)+1/(√7+√5)+.+1/√2n+1+√2n+1怎么化简
1/(√3+1)+1/(√5+√3)+1/(√7+√5)+.+1/√2n+1+√2n-1
=(√3-1+√5-√3+√7-√5+……+(√2n+1)-√(2n-1))/2
=(√(2n+1)-1)/2

1/(√2n+1+√2n-1)
= (√2n+1 - √2n-1)/2

答案是(√(2n+1)-1)/2