数列 1+1/(1*2)+1/(2*3)+···+1/(99+100)=

题目

数列 1+1/(1*2)+1/(2*3)+···+1/(99+100)=
1/(99*100)

答案

1/1*2=1/1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
每组相加,将1/2,1/3,1/4,……抵消最后只剩1-1/100=99/100