1*2+2*3+...+(n-1)*n
=(1^2-1)+(2^2-2)+(3^2-3)+……+(n^2-n)
=(1^2+2^2+3^2+……+n^2)-(1+2+3+……+n)
=n(n+1)(2n+1)/6-n(n+1)/2
=(n+1)n(n-1)/3