Explanation

(b)
We have, $\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + ...$
$= 1\sqrt{2} + 2\sqrt{2} + 3\sqrt{2} + 4\sqrt{2} + ...$
$= \sqrt{2}(1 + 2 + 3 + 4 + ...$ upto 24 terms)
$= \sqrt{2} \times \frac{24 \times 25}{2} = 300\sqrt{2}\ \ \ \ \ \ \ \ \left\lbrack \because\sum_{}^{}{n = \frac{n(n + 1)}{2}} \right\rbrack$