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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
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inequality involving increasing functions
Let $a_k$ and $b_k$ be ascending positive numbers for $1\leq k \leq K+1$.
If it is known that
$$\frac{K\left(\exp\left(\frac{1}{K}\sum_{k=1}^K b_k\right)-1\right)}{\left(\sum_{k=1}^K \sqrt{a_k} \sqrt{ …