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Results tagged with inequalities
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user 21724
for questions involving inequalities, upper and lower bounds.
6
votes
Optimal constant in Carleman's inequality
Take $a_n = \frac{1}{n}$ for $n=1,\dots,N$ and $a_n = 0$ for $n > N$. Then both sides of the inequality are $\sim e \log(N)$, hence the sharpness of the constant $e$.
- 7,249
5
votes
Accepted
A polynomial inequality
Setting $s_i = \sum_{j \leq i} x_j$, just write
$$ \sum_{i \leq n} \alpha x_i s_i^{\alpha-1} = \sum_{i \leq n} \int_{s_{i-1}}^{s_i} \alpha s_i^{\alpha-1} dt \geq \sum_{i \leq n} \int_{s_{i-1}}^{s_i} \ …
- 7,249
7
votes
A seemingly simple inequality
I have an other solution, which not as slick Markus Sprecher's one, but I think the method, which is quite general, is interesting in itself.
Fix $c \in \left]-1,1\right[$ and $n \geq 2$, and conside …
- 7,249