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

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 05:31:12

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

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.