Question

Demonstraţi inegalitatea: 1/n la pătrat < 1/(n-1) (n+1) , pentru orice "n"alarţine numerelor naturale {1}

Answer 1

[tex]\dfrac{1}{n^2}\ \textless \ \dfrac{1}{(n-1)(n+1)}\\ \text{Prin ridicare la puterea -1 obtinem:}\\ n^2\ \textgreater \ (n-1)(n+1)\\ n^2\ \textgreater \ n^2-1\\ 0\ \textgreater \ -1,adevarat\ \forall\ n\in \mathbb{N}\backslash\{1\}[/tex]