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Results tagged with inequalities
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user 47837
for questions involving inequalities, upper and lower bounds.
7
votes
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answers
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An upper bound for the difference between arithmetic and harmonic mean
Let $a_i\gt0$ for all $1\le i\le n$. It is well known that
$$
\frac{a_1+a_2+\cdots+a_n}{n}-\frac{n}{\frac{1}{a_1}+\frac{1}{a_2}+\cdots+\frac{1}{a_n}}\ge0,
$$
with the equality when all $a_i$ are equa …
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