计算1/(1+根号2)+1/(根号2+根号3)+……+1/(根号99+根号100)

问题描述:

计算1/(1+根号2)+1/(根号2+根号3)+……+1/(根号99+根号100)

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