1×2+2×3+3×4+……+n×(n+1)
=1×(1+1)+2×(2+1)+...+n×(n+1)
=1×1+2×2+.+n×n+(1+2+...+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n×(n+1)×(n+2)/3