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3
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If $\sum\limits_{k=1}^n y_k\geq n$ and $\sum\limits_{k=1}^n \frac{1}{y_k}\geq n$, then $\prod\limits_{k=1}^n y_k\geq 1$?
Let $y_1,\ldots y_n$ be positive real numbers satisfying
$y_1+\cdots+y_n\geq n$ and $\displaystyle{\frac{1}{y_1}+\cdots+\frac{1}{y_n}\geq n}$.
Is it true that $y_1y_2\cdots y_n\geq 1$?
1
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1answer
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Bound on deviation between arithmetic and harmonic mean?
It is well known that, if HM denotes the harmonic mean and AM the arithmetic mean, we have
$$ AM(x) \ge HM(x) $$
Now I am dealing with the expression
$$ \frac{1}{HM(x)} - \frac{1}{AM(x)} $$
A ...
