1/1+√2+1/√2+√3+…+1/√2013+√2014=

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/24 10:24:54
1/1+√2+1/√2+√3+…+1/√2013+√2014=1/1+√2+1/√2+√3+…+1/√2013+√2014=1/1+√2+1/√2+√3+…+1/√2013+√2014=答:分母有理化

1/1+√2+1/√2+√3+…+1/√2013+√2014=
1/1+√2+1/√2+√3+…+1/√2013+√2014=

1/1+√2+1/√2+√3+…+1/√2013+√2014=
答:
分母有理化问题:
1/1+√2+1/√2+√3+…+1/√2013+√2014
=(√2-1)/ [(√2+1)(√2-1)] +(√3-√2)/[(√3+√2)(√3-√2)+.+(√2014-√2013) / [(√2014+√2013)(√2014-√2013)
=(√2-1)+(√3-√2)+(√4-√3)+.+(√2014-√2013)
=√2014 -1