看分母,为:1+2+...+n=n(n+1)/2每个分数为2/[n(n+1)]原式=2/(1×2)+2/(2×3)+2/(3×4)+...+2/(2005×2006)=2*(1-1/2+1/2-1/3+...+1/2005-1/2006)=2*(1-1/2006)=2*2005/2006=2005/1003X没看懂