Neka su x1x_1x1, x2x_2x2, ..., xn−1x_{n-1}xn−1, xnx_nxn pozitivni realni brojevi takvi da je ∑i=1nxi=1\sum_{i=1}^{n} x_i = 1∑i=1nxi=1. Dokaži nejednakost
x12x1+x2+x22x2+x3+…+xn−12xn−1+xn+xn2xn+x1≥12.\frac{x_1^2}{x_1 + x_2} + \frac{x_2^2}{x_2 + x_3} + \ldots + \frac{x_{n-1}^2}{x_{n-1} + x_n} + \frac{x_n^2}{x_n + x_1} \geq \frac{1}{2}.x1+x2x12+x2+x3x22+…+xn−1+xnxn−12+xn+x1xn2≥21.