Question

What is the sum of n terms of the series $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+.......?$

• A. $\frac{n(n-1)}{\sqrt{2}}$
• B. $\sqrt{2}n(n+1)$
• C. $\frac{n(n+1)}{\sqrt{2}}$
• D. $\frac{n(n-1)}{2}$

Answer 1

Answer: (C)

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

Given Series: $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+.........?$

Series can be written as: $\sqrt{2}+2\sqrt{2}+3\sqrt{2}+4\sqrt{2}+......?$

$=\sqrt{2}(1+2+3+\mathrm{4.......}+uptonterms)$

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

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

Hence, C is the correct answer.