Dan je prirodni broj nnn. Dokaži da za sve realne brojeve x1,x2,…,xn≥0x_1, x_2, \ldots, x_n \geq 0x1,x2,…,xn≥0 vrijedi nejednakost
(x1+x22+⋯+xnn)⋅(x1+2x2+⋯+nxn)≤(n+1)24n(x1+x2+⋯+xn)2.\left(x_1 + \frac{x_2}{2} + \cdots + \frac{x_n}{n}\right) \cdot \left(x_1 + 2x_2 + \cdots + nx_n\right) \leq \frac{(n+1)^2}{4n} \left(x_1 + x_2 + \cdots + x_n\right)^2.(x1+2x2+⋯+nxn)⋅(x1+2x2+⋯+nxn)≤4n(n+1)2(x1+x2+⋯+xn)2.