化简1/1+√2+1/√2+√3+1/√3+√4

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 22:56:09

化简1/1+√2+1/√2+√3+1/√3+√4
化简1/1+√2+1/√2+√3+1/√3+√4

化简1/1+√2+1/√2+√3+1/√3+√4
1/(1+√2)+1/(√2+√3)+1/(√3+√4)+.+1/(√2011+√2012)
=(√2-1)/(2-1)+(√2-√3)/(2-3)+(√3-√4)/(3-4)+.+(√2011-√2012)/(2011-2012)
=-1+√2-√2+√3-√3+√4-√4+.+√2011-√2011+√2012
=√2012-1