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)
答
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