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

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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/

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.