Đặt a=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}(a> 1)\Rightarrow a^{2}=2+\sqrt{2+\sqrt{2+\sqrt{2}}}\Rightarrow 2-a^{2}=-\sqrt{2+\sqrt{2+\sqrt{2}}}
Ta có:\frac{2-\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}{2\sqrt{2+\sqrt{2+\sqrt{2}}}}=\frac{2-a}{4-a^{2}}=\frac{1}{2+a}< \frac{1}{3} ( Do a+2>3)