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-...