Question

Find the sum of $n$ terms of the series $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{16}+......$.

Answer 1

Now,

$\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+......$.

$=\sqrt{2}+\sqrt{4\times 2}+\sqrt{9\times 2}+\sqrt{16\times 2}+......$

$=\sqrt{2}+2\sqrt{2}+3\sqrt{2}+4\sqrt{2}+......$

$=\sqrt{2}(1+2+3+........)$

$=\sqrt{2}\times \frac{n(n+1)}{2}$.