Question 168
Given $n$ positive real numbers satisfying $x_1 \ge x_2 \ge \dots \ge x_n \ge 0$ and $x_1^2 + x_2^2 + \dots + x_n^2 = 1$, prove that
$$
\frac{x_1}{\sqrt{1}} + \frac{x_2}{\sqrt{2}} + \dots + \frac{x_n}{\sqrt{n}} \ge 1.
$$
$$
\frac{x_1}{\sqrt{1}} + \frac{x_2}{\sqrt{2}} + \dots + \frac{x_n}{\sqrt{n}} \ge 1.
$$