Lim ((n+1)!+(n+2)!)/((n-1)!+(n+2)!) Помогите пожалуйста!!!

Решите задачу:

$\lim\limits _{n \to \infty} \frac{(n+1)!+(n+2)!}{(n-1)!+(n+2)!} =\\\\\star\; \; (n+2)!=(n+1)!\, \cdot \, (n+2)\\\\(n+2)!=(n-1)!\, \cdot \, n\cdot (n+1)\cdot (n+2)\; \; \; \star \\\\= \lim\limkits _{n \to \infty} \frac{(n+1)!\, \cdot (1+n+2)}{(n-1)!\, \cdot (\, 1+n\cdot (n+1)\cdot (n+2)\, )} =\\\\\star \; \; (n+1)!=(n-1)!\, \cdot n\cdot (n+1)\; \; \star \\\\=\lim\limits _{n \to \infty}\frac{(n-1)!\, \cdot n\cdot (n+1)\cdot (n+3)}{(n-1)!\, \cdot (\, 1+n\cdot (n+1)\cdot (n+2)\, )} =\lim\limits _{n \to \infty}\frac{n\cdot (n+1)\cdot (n+3)}{1+n\cdot (n+1)\cdot (n+3)} =$

$= \lim\limits _{n \to \infty} \frac{n^3+4n^2+3n}{n^3+3n^2+2n+1} = \lim\limits _{n \to \infty} \frac{1+\frac{4}{n}+\frac{3}{n^2}}{1+\frac{3}{n}+\frac{2}{n^2}+\frac{1}{n^3}} =1$