How can you prove that for $n\geq1$, you have $n^n\geq e^{n-1}$? (no induction)
Proving $n^n\geq e^{n-1}$
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inequality
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0Have you tried differentiation? If that doesn't work, try series expansion of e. – 2011-03-26
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1You can write $n^n= e^z$ for some $z \in \mathbb{R}$ and then compare exponents. – 2011-03-26
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0what's wrong with induction? – 2011-03-26