计算:1/(1+√2)+1/(√2+√3)+1/(√3+√4)+…+1/(√8+√9)

来源:学生作业学帮网 编辑:学帮网 时间:2024/06/08 04:06:25

计算:1/(1+√2)+1/(√2+√3)+1/(√3+√4)+…+1/(√8+√9)

1/(1+√2)+1/(√2+√3)+1/(√3+√4)+1/(√4+√5)+···+1/(√8+√9)
=(√2-1)/(2-1)+(√3-√2)/(3-2)+(√4-√3)/(4-3)+···+(√9-√8)/(9-8)
=(√2-1)+(√3-√2)+(√4-√3)+(√5-√4)+···+(√9-√8)
=-1+√9
=-1+3
=2.