Question 415088
{{{((n+2)!(n-2)!-(n+1)!(n-1)!)/((n)!(n-3)!)}}}
...........{{{(n+2)!=n!*(n+1)*(n+2)}}}
...........{{{(n+1)!=n!*(n+1)}}}
...........{{{(n-2)!=(n-3)!*(n-2)}}}
...........{{{(n-1)!=(n-3)!*(n-2)*(n-1)}}}
{{{((n+2)!(n-2)!-(n+1)!(n-1)!)/((n)!(n-3)!)=(n!*(n+1)*(n+2)*(n-3)!*(n-2)-n!*(n+1)*(n-3)!*(n-2)*(n-1))/((n)!(n-3)!)=(n!(n-3)!((n+1)*(n+2)*(n-2)-(n+1)*(n-2)*(n-1)))/((n)!(n-3)!)=(n+1)*(n+2)*(n-2)-(n+1)*(n-2)*(n-1)=(n+1)(n^2-4)-(n-2)(n^2-1)=n^3-4n+n^2-4-n^3+n+2n^2-2=3n^2-3n-6}}}