n=k+1时
1×(k+1)＋2×k＋3(k－1)＋……(k+1)×1
=1×k＋2×(k－1)＋3(k－2)＋……k×1+(1+2+3+...k+k+1)
=k(k+1)(k+2)/6+(1+k)(2+k)/2
=(k+1)(k+2)(k+3)/6