2. Suppose that $\displaystyle K > 1\,\& \,x_{K - 1} < x_K < 2$ is true.
$\displaystyle \begin{array}{rclcl} {x_{K - 1} + 2} & < & {x_K + 2} & < & 4 \\ {\sqrt {x_{K - 1} + 2} } & < & {\sqrt {x_K + 2} } & < & {\sqrt 4 } \\ {x_K } & < & {x_{K + 1} } & < & 2 \\ \end{array}$