1/12+1/20+1/30+.+1/90+1/110＝1/(3×4)+1/(4×5)+1/(5×6)+.+1/(9×10)+1/(10×11)=(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+.+(1/9-1/10)+(1/10-1/11)=1/3-1/11=8/33关键是拆项1/（n×（n+1））=1/n-1/(n+1)希望我的回答对...