Inegalitate by Vasile Popa

[BogdanCNFB]

Fie \( p,n\in N^{*},n\ge 3 \). Sa se demonstreze inegalitatea:
\( (p-\frac{p-1}{n})\cdot (p-\frac{2p-1}{n})\cdot ... \cdot(p-\frac{pn-1}{n})>\frac{1}{n!} \)
si apoi sa se deduca inegalitatea \( (n!)^2>n^n \).

[Marius Damian]

\( p-\frac{kp-1}{n}>\frac{1}{k}, \forall k= \overline{1,n}. \)