计算:1/2+5/6+11/12+……+109/110=

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

1/2+5/6+11/12+ 109/110
=1/2+1-1/6+...+1-1/110
=1/2+1-1/2+1/3+1-1/3+1/4+...+1-1/10+1/11
=9+1/11
=100/11

1/2+5/6+11/12+……+109/110
=(1-1/2)+(1-1/6)+...+(1-1/110)
=10-(1/2+1/6+...+1/110)
=10-[(1-1/2)+(1/2-1/3)+...+(1/10-1/11)]
=10-(1-1/11)
=9+1/11
=100/11