OMath! - Inequalities

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Important Threads
	$\forall n \in \mathbf{N}^+, \forall x\in (0,\pi) \left(\displaystyle{\sum_{k=1}^n \frac {1}{k} \sin kx > 0} \right)$ elim	1	4,021	1 Vote(s) - 2 out of 5 in Average	03-05-2010 12:25 PM Last Post: elim
Normal Threads
	$(0 < m\le a_k/b_k \le M)\implies \|A\|\|B\|\le{\small\dfrac{m + M}{2\sqrt{mM}}}(A\cdot B)$ elim	1	7,947	0 Vote(s) - 0 out of 5 in Average	12-15-2012 05:30 AM Last Post: elim
	$e\cdot n! - \lfloor e\cdot n! \rfloor < 1/n$ elim	0	3,021	0 Vote(s) - 0 out of 5 in Average	03-31-2011 11:11 AM Last Post: elim
	An inequality about floor function elim	0	3,011	0 Vote(s) - 0 out of 5 in Average	03-04-2010 04:07 PM Last Post: elim
	An integral inequality elim	1	3,756	0 Vote(s) - 0 out of 5 in Average	05-10-2010 12:52 AM Last Post: elim
	Bernstein's Theorem (Polynomial norms inequality) elim	1	5,263	0 Vote(s) - 0 out of 5 in Average	08-11-2010 10:53 AM Last Post: elim
	Inequalities for $ a,b,c > 0$ or $ x,y,z > 0$ admin	0	2,974	0 Vote(s) - 0 out of 5 in Average	03-15-2010 10:24 AM Last Post: admin
	Inequalities of 3 positive numbers elim	0	2,541	0 Vote(s) - 0 out of 5 in Average	04-14-2010 02:21 PM Last Post: elim
	Inequalities when (0 < a,b,c and a+b+c=1) elim	0	2,397	0 Vote(s) - 0 out of 5 in Average	03-14-2010 01:17 AM Last Post: elim
	Inequalities with $n$ variables such as $\sum_{i=1}^n\sum_{j=1}^n (x_i x_j )/(i+j) \ge 0\; \cdots$ elim	0	2,401	0 Vote(s) - 0 out of 5 in Average	10-08-2010 12:38 PM Last Post: elim
	Power of $(\sqrt{2} +1)$ and floor function elim	0	2,571	0 Vote(s) - 0 out of 5 in Average	01-07-2011 07:24 PM Last Post: elim
	Show that $(x,a_k \in [-1,1], \sum_{k=1}^n a_k = 0) \Rightarrow (\sum_{k=1}^n \|x-a_k\| \leq n)$ elim	1	3,572	0 Vote(s) - 0 out of 5 in Average	03-18-2010 06:59 PM Last Post: elim
	Some inequalities require special tricks...$a,b>0 \Rightarrow a^b + b^a > 1$ elim	0	2,449	0 Vote(s) - 0 out of 5 in Average	12-07-2010 01:09 PM Last Post: elim
	Strange $a,b,c \in \mathbb{N}^+$ and $41/42$ elim	1	3,210	0 Vote(s) - 0 out of 5 in Average	05-07-2010 10:59 AM Last Post: elim
	[T]:$a^2+b^2+c^2-(1/2)(\|a-b\|+\|b-c\|+\|c-a\|)^2\geq 4S\sqrt{3}$ for triangles with side lengths $a,b,c$ and area $S$ elim	0	2,416	0 Vote(s) - 0 out of 5 in Average	04-12-2010 10:15 AM Last Post: elim

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