析：1°,当n=1时1x4=1x2x2显然成立;2°,假设当n=k时等式成立,即1x4+2x7+3x10+...+n(3k+1)=k(k+1)²则当n=k+1时,左边=1x4+2x7+3x10+...+k(3k+1)+(k+1)[3(k+1)+1]=k(k+1)²+(k+1)[3(k+1)+1]=(k+1)(k²+k+3...