Answer by Aig for Prove the following from Jensen's inequality
$$n \cdot \left( \frac{n+1}{2} \right)^{ \frac{n+1}{2} } \le \sum_{k=1}^{n} k^k$$$$\left( \frac{n+1}{2} \right)^{ \frac{n+1}{2} } \le \frac{\sum_{k=1}^{n} k^k}n$$$$\left( \frac{n(n+1)}{2n} \right)^{...
View ArticleProve the following from Jensen's inequality
$n \cdot \left( \frac{n+1}{2} \right)^{\left( \frac{n+1}{2} \right)} \leqslant \sum_{k=1}^{n} k^k \text{ for } n \in \mathbb{N}$I've tried to transform the left part of inequality, but nothing worked...
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