Rebecca Villa

2022-07-04

For all positive integer $n\ge 8$,
$⌊\sqrt{n!}⌋=⌊\sqrt{n!+2}⌋,$
where the symbol $⌊x⌋$ indicates the floor function.

SweallySnicles3

Expert

Use $\sqrt{a+2}=\sqrt{a}\ast \sqrt{1+2/a}<\sqrt{a}\ast \left(1+2/a\right)$