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