因为1/(1×2)=1-1/2,1/(2×3)=1/6-1/2-1/3,...所以 1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+...+1/(9×10) =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10（相邻两个校区,得：） =1-1/10 =9/10 请采纳回答...