n=1时,左边=1*1=1右边=1/6*1*2*3=1左边=右边,等式成立!假设n=k时成立 (k>1)即:1*k+2(k-1)+3(k-2)+…+(k-1)*2+k*1=(1/6)k(k+1)(k+2)当n=k+1时；左边=1*(k+1)+2(k+1-1)+3(k+1-2)+…+(k+1-1)*2+(k+1)*1=1*k+1*1+2(k-1)+...