(1!+2!+3!+...+n!)/n!..
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(1!+2!+3!+...+n!)/n!..(1!+2!+3!+...+n!)/n!..(1!+2!+3!+...+n!)/n!..1*2-1+2*3-2+3*4-3……+n(n+1)-n=[1*2+
(1!+2!+3!+...+n!)/n!..
(1!+2!+3!+...+n!)/n!..
(1!+2!+3!+...+n!)/n!..
1*2-1+2*3-2+3*4-3……+n(n+1)-n=[1*2+2*3+3*4+…+n(n+1)]-(1+2+3+……+n)=1/3(1*2*3-0*1*2)+1/3(2*3*4-1*2*3)+…1/3[n*(n+1)(n+2)-(n-1)n(n+1)]-(1+2+3+……+n)
=1/3[n(n+1)(n+2)]-[(n+1)n]/2
=[n(n+1)(2n+1)]/6
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