\(\qquad\)Let \(n \ge 3\) be an integer. Let \(t_1, t_2, \ldots, t_n\) be positive real numbers such that $$ n^2 + 1 > (t_1 + t_2 + \ldots + t_n) \left(\frac1{t_1}+\frac1{t_2}+\dots+\frac1{t_n}\right). $$ \(\qquad\)Show that \(t_i, t_j , t_k\) are side lengths of a triangle for all \(i, j, k\) with \(1 \le i \lt j \lt k \le n\).
| Attributes | Олімпіадна |
|---|---|
| Source | International Mathematical Olympiad |
| Year | 2004 |
| Number | 4 |
| Difficulty | 10.0 |
| Themes |