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The Cauchy-Schwarz inequality states $|\langle x,y \rangle |\leq ||x||\cdot ||y||.$ Use this tag for questions related to the CS inequality and its applications.

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A plausible inequality

[Wrong ounter-example deleted] This it true for all $n$. The case $n=2$ is handled by Hailong Dao, let's reduce the general case to $n=2$. First, we may assume that $a_1=1$ and $a_n=0$ as others men …
Sergei Ivanov's user avatar