Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Given series is $\sqrt{2}+2\sqrt{2}+3\sqrt{2}+4\sqrt{2}+.....=\sqrt{2}[1+2+3+4+....tonterm]\sqrt{2}(\sum n)=\sqrt{2}\frac{n(n+1)}{2}=\frac{n(n+1)}{2}$