Question

Sa se rezolve inecuatia C de n luate cate 2 < 10 , n ≥2 , n natural.

Answer 1

[tex]C_{n}^2 \ \textless \ 10, n\geq 2, n\in N\\ \\ \frac{n!}{2!\cdot (n-2)!}\ \textless \ 10\\ \frac{(n-2)!\cdot(n-1)\cdot n}{2\cdot (n-2)!}\ \textless \ 10\\ (n-1)\cdot n\ \textless \ 20\\ n^2-n-20\ \textless \ 0\\ \Delta=1+4\cdot20=81\\ n_1=\frac{1+9}{2}=5\\ n_2=\frac{1-9}{2}=-4\\ (5;-4)\cap N=\{0,1,2,3,4\}\\ Cum: n\geq 2\Rightarrow S:n\in \{2,3,4\}[/tex]