1/3+1/6+1/12+...+1/9900

分类: 作业答案 • 2022-04-17 21:36:03

问题描述：

答

1/2+1/6+1/12+...+1/9900
=1/1*2+1/2*3+1/3*4+1/4*5……+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100
中间正负抵消
=1-1/100
=99/100