$$\mathop {\lim }\limits_{x \to 1} {\left( {{{1 + x} \over {2 + x}}} \right)^{{{(1 - \sqrt x )} \over {(1 - x)}}}}$$ is equal to

The value of

$$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt {n + 1} + \sqrt {n + 2} + ... + \sqrt {2n - 1} } \over {{n^{3/2}}}}} \right\}$$ is