=n*1+(n-1)*2+(n-2)*3+....+(n-(n-1))*n
=(1+2+3+...+n)*n-(1*2+2*3+3*4+...+(n-1)*n)
=n^2(n+1)/2-((1^2-1)+(2^2-2)+(3^2-3)+……+(n^2-n))
=n^2(n+1)/2-((1^2+2^2+3^2+……+n^2)-(1+2+3+……+n))
= n^2(n+1)/2-(n(n+1)(2n+1)/6-n(n+1)/2)
=n^2(n+1)/2-n(n+1)(2n+1)/6+n(n+1)/2
=(n+1)(3n^2-2n^2-n+3n)/6
=(n+1)(n^2+2n)/6
=n(n+1)(n+2)/6
=n
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