# Questions tagged [lower-bounds]

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### is it possible to prove this :$\sum_{n\le X}\tan(n!)=\mathcal{O}(X^{\alpha})$?, $\alpha <1$?

This series $\sum_{n\geq 0}\tan(n!)$ probably diverges. I want to find a polynomial bounding $|\sum_{n\le X}\tan(n!)|$. Is it possible to prove that $\sum_{n\le X}\tan(n!)=\mathcal{O}(X^{\alpha})$ ...
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### Is this lower bound for the size of minimal vertex cover new/interesting?

I have found this lower bound for the size of minimal vertex cover (and proved it). If a simple connected graph G on n vertices has largest and smallest eigenvalues $\lambda_1,\lambda_n$, ...
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### Fast computation of a ball with radius r with largest number of input points

We are given a set S of n points equipped with some metric and an integer $r>0$. We define $B(x,r) \subseteq S$ (the ball with radius r centered in x) to be the set of points in S within distance r ...