∵an=n×（n+3）=n2+3n，∴Sn=a1+a2+a3+…+an=（1+3×1）+（4+3×2）+（9+3×3）+…+（n2+3n）=（12+22+32+…+n2）+3（1+2+3+…+n）= n(n+1)(2n+1) 6 + 3n(n+1) 2 = n(n+1)(n+5) 3 ．答案： n(n+1)(n+5) 3 ．
