数列 1+1/(1*2)+1/(2*3)+···+1/(99+100)=1/(99*100)
问题描述：
数列 1+1/(1*2)+1/(2*3)+···+1/(99+100)=
1/(99*100)
答
1+1/(1*2)+1/(2*3)+···+1/(99+100)=1+1/1-1/2+1/2-2/3+2/3-3/4...-1/99+1/99-1/100=199/100
答
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