Question

计算：1/1+根号3+1/根号3+根号5+---1/根号9+根号11

Answer 1

1/(1+√3)+1/(√3+√5)+……+1/(√9+√11)

=(√3-1)/[(√3+1)(√3-1)]+(√5-√3)/[(√5+√3)(√5-√3)]+……+(√11-√9)/[(√11+√9)(√11-√9)]

=(√3-1)/2+(√5-√3)/2+……+(√11-√9)/2

=(√3-1+√5-√3+√7-√5+√9-√7+√11-√9)/2

=(√11-1)/2