分类：教育/科学-院校信息
问题：一道分数的巧算 
回答：1/2+5/6+11/12+19/20+........109/110 =1-1/2+1-1/6+1-1/12+1-1/20+......+1-1/110 =10-(1/2+1/6+1/12+1/20+......+1/110) =10-(1/1*2+1/2*3+1/3*4+1/4*5+......+1/10*11) =10-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/10-1/11) =10-(1-1/11) =10-10/11 =100/11