Question 4
Let $n \ge 3$ be an integer and $t_1$, $t_2$, …, $t_n$ positive real numbers such that $$
n^2+1 \gt \left(t_1 + t_2 + \dots + t_n\right)
\left( \frac{1}{t_1} + \frac{1}{t_2} + \dots + \frac{1}{t_n} \right).
$$ Show that $t_i$, $t_j$, $t_k$ are the sides of a triangle for all $i$, $j$, $k$ with $1 \le i \lt j \lt k \le n$.
n^2+1 \gt \left(t_1 + t_2 + \dots + t_n\right)
\left( \frac{1}{t_1} + \frac{1}{t_2} + \dots + \frac{1}{t_n} \right).
$$ Show that $t_i$, $t_j$, $t_k$ are the sides of a triangle for all $i$, $j$, $k$ with $1 \le i \lt j \lt k \le n$.