Question 41
Determine all integers $n \gt 1$ for which the inequality
$$
x_1^2 + x_2^2 + \dots + x_n^2 \geq (x_1 + x_2 + \dots + x_{n-1})x_n
$$
holds for all real $x_1, x_2, \dots, x_n$.
$$
x_1^2 + x_2^2 + \dots + x_n^2 \geq (x_1 + x_2 + \dots + x_{n-1})x_n
$$
holds for all real $x_1, x_2, \dots, x_n$.