[tex]c)\frac{(n+3)!}{(n+1)!}=20,n\in \mathbb{N}^*\\
\frac{(n+1)!\cdot(n+2)\cdot(n+3)}{(n+1)!}=20\\
(n+2)(n+3)=20\\
n^2+2n+3n+6=20\\
n^2+5n-14=0\\
n^2+7n-2n-14=0\\
n(n+7)-2(n+7)=0\\
(n+7)(n-2)=0\Rightarrow n_1=-7(nu\ convine\ deoarece\ -7\notin \mathbb{N})\\
~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow n_2=2\\
S:n=2[/tex]
[tex]d)3n(n+1)!=(n+2)!,n\in \mathbb{N}^*\\
3n(n+1)!=(n+1)!\cdot (n+2)\\
3n=n+2\\
2n=2\\
n=1\in \mathbb{N}\\
S:n=1[/tex]
