Determine all the integers $n > 1$ such that $$\sum_{i=1}^{n}x_i^2 \ge x_n \sum_{i=1}^{n-1}x_i$$for all real numbers $x_1, x_2, ... , x_n$.
Source: 2001 Singapore TST 2.2
Tags: inequalities, algebra
Determine all the integers $n > 1$ such that $$\sum_{i=1}^{n}x_i^2 \ge x_n \sum_{i=1}^{n-1}x_i$$for all real numbers $x_1, x_2, ... , x_n$.