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1x2+2x3+3x4+······+n(n+1)
=1x(1+1)+2x(2+1)+3x(3+1)+········+n(n+1)
=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(n+1)(n+2)/3
=1x(1+1)+2x(2+1)+3x(3+1)+········+n(n+1)
=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(n+1)(n+2)/3
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