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How do I know

$$\frac{\ln{n}}{n}\ge\frac{1}{n}$$

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False if $n=1$ or $n=2$; but if $n\geq 3$, it follows from the fact that $n\geq e$, hence $\ln (n)\geq 1$. –  Arturo Magidin Mar 15 '12 at 3:25

2 Answers 2

up vote 3 down vote accepted

Because you cross multiply to get $n \ln n \geq n$? (so that you also know it's only true for $n \geq 3$ as well)

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$\ln n \geq 1$ when $n\geq 3$. So it is true when $n\geq 3$.

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