Show that:
$\displaystyle 2! \cdot 4! \cdot... \cdot(2n)!>[(n+1)!]^n $ for $n>1$ where $n$ is natural
I tried by induction but I stuck when I have to show that:
$(2n+2)!>(n+2)!(n+2)^n$
2026-04-06 09:00:02.1775466002
Prove inequality holds
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Use that $\frac{(2n+2)!}{(n+2)!}=(n+3)(n+4)...(2n+2)>(n+2)...(n+2)$