How to prove that following inequality is not true for any natural number $n\ge 5$
$$2\left\lfloor \frac{n}{3}\right\rfloor-2>n-1-\sqrt{(n+1)^2-4(n-1)\left\lfloor \frac{n-1}{2}\right\rfloor+4\left\lfloor \frac{n-3}{2}\right\rfloor^2}$$
2026-03-30 01:15:51.1774833351
Inequality involving greatest integer function
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