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 $n \ge 2,$, $$\sqrt {n\left( {n + 1} \right)} < n + 1.$$

Question

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 $n \ge 2,$, $$\sqrt {n\left( {n + 1} \right)} < n + 1.$$

Statement - 1 is false, Statement - 2 is true

Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for statement - 1

Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1

Statement - 1 is true, Statement - 2 is false

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