Problem

Source: Ukraine 1997 grade 9

Tags: inequalities, induction, inequalities unsolved



For every natural number $ n$ prove the inequality: $ \sqrt{2+\sqrt{2+\sqrt{2+...+\sqrt{2}}}}+\sqrt{6+\sqrt{6+\sqrt{6+...+\sqrt{6}}}}<5$ where there are $ n$ twos and $ n$ sixs on the left hand side.