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Kroasia TST

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Misalkan $n\ge 1$ dan $x_1,\dots,x_n \ge 0 $. Buktikan bahwa
$$ (x_1 + \frac{x_2}{2} + \ldots + \frac{x_n}{n}) (x_1 + 2x_2 + \ldots + nx_n) \le \frac{(n+1)^2}{4n} (x_1 + x_2 + \ldots + x_n)^2 .$$

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