An inequality

General Mathematics
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Riemann
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Joined: Sat Nov 14, 2015 7:32 am
Location: Melbourne, Australia

An inequality

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Let $x, y, z$ be positive real numbers. Prove that:

$$ \sqrt{\frac{x}{x+y}} + \sqrt{\frac{y}{y+z}} + \sqrt{\frac{z}{z+x}} \leq \frac{3}{\sqrt{2}}$$
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$

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