1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36 + 1/45 + 1/55=?

问题描述:

1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36 + 1/45 + 1/55=?
规律是?

规律略原式=2*(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110)=2*(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11)=2*(1/2-1/11)=2*9/22=9/11