1/2+5/6+11/12+19/20+……+89/90+109/110=1-1/2+1-1/6+1-1/12...+1-1/110=10-(1/2+1/6+1/12...+1/110)=10-(1/2+1/2-1/3+1/3-1/4+1/5-1/5...+1/10-1/11)=10-10/11=100/11