计算(1/1+根号2+1/根号2+根号3+1/根号3+根号4+...+1/根号 n+根号n+1)(根号n+1+1)
问题描述:
计算(1/1+根号2+1/根号2+根号3+1/根号3+根号4+...+1/根号 n+根号n+1)(根号n+1+1)
答
=[√2-1+ √3-√2+√4-√3+……+√(n+1)-√n][√(n+1)+1] =[√(n+1)-1][√(n+1)+1] =n+1-1 =n