Q. The sum to $n$ terms of the series $2^{2} + 4^{2} + 6^{2} + ...$ is
A) $\frac{n(n + 1)(2n + 1)}{3}$
B) $\frac{2n(n + 1)(2n + 1)}{3}$
C) $\frac{n(n + 1)(2n + 1)}{6}$
D) $\frac{n(n + 1)(2n + 1)}{9}$
Explanation
(b)
$2^{2} + 4^{2} + 6^{2} + ... + (2n)^{2}$
$= 2^{2}\left( 1^{2} + 2^{2} + \ldots + n^{2} \right)$
$= \frac{4n(n + 1)(2n + 1)}{6}$
$= \frac{2n(n + 1)(2n + 1)}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.