Quadratic Equation and Inequalities

STATEMENT - 1 : For every natural number $n \ge 2,$ ${1 \over {\sqrt 1 }} + {1 \over {\sqrt 2 }} + ........ + {1 \over {\sqrt n }} > \sqrt n .$ STATEMENT - 2 : For every natural number $n \ge 2,$, $\sqrt {n\left( {n + 1} \right)} < n + 1.$$