化简:1/(√3+1)+1/(√5+√3)+1/(√7+√5)+····+1/[(√2n+1)+(√2n-1)]

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/15 19:51:14
化简:1/(√3+1)+1/(√5+√3)+1/(√7+√5)+····+1/[(√2n+1)+(√2n-1)]化简:1/(√3+1)+1/(√5+√3)+1/(√7+√5)+····+1/[(√2n

化简:1/(√3+1)+1/(√5+√3)+1/(√7+√5)+····+1/[(√2n+1)+(√2n-1)]
化简:1/(√3+1)+1/(√5+√3)+1/(√7+√5)+····+1/[(√2n+1)+(√2n-1)]

化简:1/(√3+1)+1/(√5+√3)+1/(√7+√5)+····+1/[(√2n+1)+(√2n-1)]
1/(√3+1)+1/(√5+√3)+1/(√7+√5)+····+1/[(√2n+1)+(√2n-1)]
采用分母有理化,
=(√3-1)+(√5-√3)+……+【√(2n+1)-√(2n-1)】
=√(2n+1)-1