1*2+2*3+...+n(n +1)=1²+1+2²+2+.+n²+n=(1^2+2^2+...+n^2)+(1+2+3+.+n)=[n(n+1)(2n+1)]/6+n(n+1)/2=n(n+1)/6 *[2n+1+3]=n(n+1)(n+2)/3望采纳谢谢
1×2×3×4×5×……×n×（n+1）=（n+1）！
