1/1+√2+1/√2+√3+…+1/√2013+√2014=

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 00:53:27
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=

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