求和n*(1*2)+(n-1)*(2*3)+(n-2)*(3*4)+...+2*(n-1)*n+n*(n+1)

问题描述:

求和n*(1*2)+(n-1)*(2*3)+(n-2)*(3*4)+...+2*(n-1)*n+n*(n+1)

=n*(1*2+2*3+3*4+...+n*(n+1)) - (0*1*2-1*2*3-2*3*4-...-(n-1)n(n+1))
=n*n*(n+1)*(n+2)/3-(n-1)n(n+1)(n+2)/4
=n(n+1)(n+2)(n+3)/24.