Question

AJUTOR??? EX 3 PUNCTELE C ȘI D

Answer 1

[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]