1/3+1/8+1/15...+1/99

来源：百度知道 编辑：UC知道 时间：2024/05/30 03:03:50
等于?
规律是?

36/55

1/3+1/8+1/15+1/(5×5-1)+1/(6×6-1)+1/(7×7-1)+1/99+1/99
=1/3+1/8+1/15+1/24+1/35+1/48+1/65+1/80+1/99
=?
我这个规律也对吧，只不过答案好复杂，估计是你们那个规律正确

36/55

原式等于1/2*[(1-1/3)+(1/2-1/4)+.....(1/9-1/11)=1/2*(1+1/2-1/10-1/11)=7/10

1/3+1/8+1/15...+1/99
=1/（1*3）+1/（2*4）+1/（3*5）+……+1/(9*11)
=1/2(1-1/3+1/2-1/4+1/3-1/5+……+1/8-1/10+1/9-1/11)
=1/2(1+1/2-1/10-1/11)
=36/55