1、当n=1时,左边1*（3*1+3）=6=1*(1+1)(1+2)=右边2、假设当n=k时,等式成立.所以当n=k+1时,左边=6+2*9+3*12+…+k(3k+3)+(k+1)[3(k+1)+3]=6+2*9+3*12+…+k(3k+3)+(k+1)(3k+6)=k(k+1)(k+2)+(k+1)(3k+6)=(k+1)(k^2+5k+6...