Question

The sum of $ 24 $ terms of the following series $ \sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\ldots $ is

• A. $ 300 $
• B. $ 300\sqrt{2} $
• C. $ 200\sqrt{2} $
• D. none of these

Answer 1

Answer: (B)

$\Sigma n=\frac{n(n+1)}{2}$
We have $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\ldots$
$\quad=1 \sqrt{2}+2 \sqrt{2}+3 \sqrt{2}+4 \sqrt{2}+\ldots$
$=\sqrt{2}(1+2+3+4+\ldots$ upto 24 terms $)$
$=\sqrt{2} \times \frac{24 \times 25}{2}$
$=300 \sqrt{2}$