计算:1/2+5/6+11/12+19/20+……+89/90+109/110= 你怎么知道有9项?

1/2+5/6+11/12+19/20+……+89/90+109/110=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+。+(1-1/90)+(1-1/110)=1-1/2+1-1/6+1-1/12+1-1/20+。+1-1/90+1-1/110=1-(1-1/2)+1-(1/2-1/3)+1-(1/3-1/4)+1-(1/4-1/5)+。+1-(1/9-1/10)+1-(1/10-1/11)=1*9-1+1/2-1/2+1/3-1/3+1/4-1/4+1/5+。-1/9+1/10-1/10+1/11(因为从2开始到11结束,所以有9项)=9-1+1/11=8又1/11