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Inequalities with $n$ variables such as $\sum_{i=1}^n\sum_{j=1}^n (x_i x_j )/(i+j) \ge 0\; \cdots$
10-08-2010, 12:38 PM
Post: #1
Inequalities with $n$ variables such as $\sum_{i=1}^n\sum_{j=1}^n (x_i x_j )/(i+j) \ge 0\; \cdots$
(1)$\displaystyle{\sum_{i=1}^n\sum_{j=1}^n \frac{x_i x_j }{i+j }\ge 0}, \quad \forall x_i \in \mathbb{R}$. Equality holds iff $x_i = 0,\quad i=\overline{1,n}$
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