证明：(1)当n=1时,左边=4,右边=4,等式成立.(2)假设n=k时等式成立,即2+4+6+…+(2k)=（2/3)k(k+1)(2k+1).那么,2+4+6+…+(2k)+[2(k+1)]=(2/3)k(k+1)(2k+1)+[2(k+1)]=(2/3)k(k+1)(2k+1)+4(k+1)(k+1)=2(k+1...