K!*(k+1) (k-1)!*K*(k+1) (k-5)!*(K^2-7K+12)

Решите задачу:

$k!\cdot (k+1)=(k+1)!\\\\(k-1)!\cdot k\cdot (k+1)=(k+1)!\\\\(k-5)!\cdot (k^2-7k+12)=(k-5)!\cdot (k-4)(k-3)=(k-3)!\\\\ \frac{P_{n+1}}{P_{n+3}} = \frac{(n+1)!}{(n+3)!} = \frac{(n+1)!}{(n+1)!(n+2)(n+3)} = \frac{1}{(n+2)(n+3)} = \frac{1}{n^2+5n+6} \\\\ \frac{(k+4)!(k+5)}{(k-6)!} = \frac{(k-6)!(k-5)(k-4)(k-3)(k-2)(k-1)k(k+1)(k+2)(k+3)(k+4)(k+5)}{(k-6)!} =\\\\=(k-5)(k-4)(k-3)(k-2)(k-1)k(k+1)(k+2)(k+3)\cdot \\\\\cdot (k+4)(k+5)$