[tex] \frac{n!}{(n-2)!}<6\\ \frac{(n-2)!(n-1)n}{(n-2)!}<6\\(n-1)n<6\\n^2-n-6<0\\\triangle=1+24=25\\n_{1/2}= \frac{1\pm5}{2} \\n_{1}=3\\n_{2}=-2\\ n\in(-2,3)\\n\inN=>n\in\{0,1,2\}\\n! \ exista\ pentru\ n \geq 0\\(n-2) ! \ exista\ pentru\ n-2 \geq 0=>n \geq 2\\Concluzie:n=2\\Verificare\\ \frac{2!}{(2-2)!}<6\\ \frac{2}{1} <6(Adevarat)[/tex]
