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• 17:50, 17 September 2025 Andrei.Horvat talk contribs created page 23964 (Created page with "'''23964 (Marin Bancoș)''' ''Să de demonstreze inegalitatea <math display="block"> \sum_{i=2}^{n} \sqrt[i]{\left(i!\right)^2} < \frac{2n^3+9n^2+13n-24}{24} .</math>'' '''Soluție''' Pentru orice număr natural <math>n</math>, cu <math> n\ge 2</math> are loc inegalitatea <math display="block"> \sqrt[n]{n!} = \sqrt[n]{1\cdot 2\cdot \ldots \cdot n} < \frac{1+2+\ldots+n}{n} = \frac{n+1}{2}.</math> Atunci <math display="block"> \sum_{i=2}^{n} \sqrt[i]{\left(I!\right)...")