Question 38
Let $d_1, d_2, \dots, d_n$ be nonnegative real numbers satisfying $1 \ge d_1 \ge \dots \ge d_n \ge 0$. Prove
$$
\frac{(1 + d_1 + d_2 + \dots + d_n)^2}{n + 1} \ge 2 \cdot \frac{d_1^2 + 2d_2^2 + \dots + n d_n^2}{n}.
$$
$$
\frac{(1 + d_1 + d_2 + \dots + d_n)^2}{n + 1} \ge 2 \cdot \frac{d_1^2 + 2d_2^2 + \dots + n d_n^2}{n}.
$$