解 1/n(n+1)(n+2)=[1/n-1/n+1](1/n+1)=1/n(n+1)-1/(n+1)(n+2)=1/2(1/n-1/n+2)-1/n+1+1/n+2=1/2[1/n+1/n+2-2/n+1]=1/2[1/n-1/n+1+1/n+2-1/n+1]所以 1/1*2*3 +1/2*3*4+...+1/n(n+1)(n+2)=1/2(1-1/2+1/3-1/2+1/2-1/3+1/...