计算:1/(1+根号2)+1/(根号2+根号3)+1/(根号3+根号4)+.+1/(根号99+根号100)

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/01 14:27:44
计算:1/(1+根号2)+1/(根号2+根号3)+1/(根号3+根号4)+.+1/(根号99+根号100)

计算:1/(1+根号2)+1/(根号2+根号3)+1/(根号3+根号4)+.+1/(根号99+根号100)
计算:1/(1+根号2)+1/(根号2+根号3)+1/(根号3+根号4)+.+1/(根号99+根号100)

计算:1/(1+根号2)+1/(根号2+根号3)+1/(根号3+根号4)+.+1/(根号99+根号100)
1/(1+根号2)+1/(根号2+根号3)+1/(根号3+根号4)+.+1/(根号99+根号100)
=√2-1+√3-√2+√4-√3+.+√100-√99
=√100-1
=10-1
=9