Explanation

(c)
$\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + ...$
$1 \times \sqrt{2} + 2\sqrt{2} + 3\sqrt{2} + 4\sqrt{2} + ...$
$= \sqrt{2}(1 + 2 + 3 + 4 + ...upto\ 24\ terms)$
$= \sqrt{2} \times \frac{24 \times 25}{2} = 300\sqrt{2}\ \ \ \ \left\lbrack \because\Sigma n = \frac{n(n = 1)}{2} \right\rbrack$