1/2加1/6加1/12加1/20加···加1/9

1/2加1/6加1/12加1/20加···加1/9000简便方法计算

1个回答

注：末项书写有误,估计1/9000为1/9900.
原式=1/(1*2)+1/(2*3)+1/(3*4)+…+1/(99*100)
=1-1/2+1/2-1/3+1/3-1/4+…+1/99-1/100
=1-1/100
=99/100