化简1/1+√2+1/√2+√3+...+1/√8+√9

问题描述:

化简1/1+√2+1/√2+√3+...+1/√8+√9

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