Question

Докажите неравенство на фото!!!

Answer 1

$big( sqrt{2+ sqrt{2+ sqrt{ 2+sqrt{2}}}}~big)^2 textless 2^2 \ 2+ sqrt{2+ sqrt{ 2+sqrt{2}}} textless 4 \big( sqrt{2+ sqrt{ 2+sqrt{2}}}big~)^2 textless 2^2 \ 2+ sqrt{ 2+sqrt{2}} textless 4\big(sqrt{2+sqrt{2}}big~)^2 textless 2^2 \2+sqrt{2} textless 4 \ (sqrt{2})^2 textless 2^2 \ 2 textless 4$

Неравенство доказано.