Cho $\it{x}_{\,\it{i}}= \it{x}_{\,\it{i}+ \it{n}}> \it{0}\,\,\left ( \it{i}= \overline{\it{1},\,\it{n}}\,,\,\,\it{n}\geqq \it{3} \right )$ . Chứng minh rằng :
$\sum\limits_{\it{i}= \it{1}}^{\it{n}}\,\frac{\it{x}_{\,\it{i}}}{\it{x}_{\,\it{i}}+ \it{x}_{\,\it{i}+ \it{1}}}\,\sum\limits_{\it{i}= \it{1}}^{\it{n}}\,\frac{\it{x}_{\,\it{i}}+ \it{x}_{\,\it{i}+ \it{1}}}{\it{x}_{\,\it{i}}}\leqq \it{n}\,\sum\limits_{\it{i}= \it{1}}^{\it{n}}\,\frac{\it{x}_{\,\it{i}}}{\it{x}_{\,\it{i}+ \it{1}}}$