Question 90
Determine the smallest real constant $c$ such that
$$
\sum_{k=1}^{n} \left( \frac{1}{k} \sum_{j=1}^{k} x_j \right)^2 \le c \sum_{k=1}^{n} x_k^2,
$$
for all positive integers $n$ and all positive real numbers $x_1, \dots, x_n$.
$$
\sum_{k=1}^{n} \left( \frac{1}{k} \sum_{j=1}^{k} x_j \right)^2 \le c \sum_{k=1}^{n} x_k^2,
$$
for all positive integers $n$ and all positive real numbers $x_1, \dots, x_n$.