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Question: Answered & Verified by Expert
The sum to $n$ terms of the series $2^2+4^2+6^2+$\ldots\ldotsis
MathematicsSequences and SeriesJEE Main
Options:
  • A $\frac{n(n+1)(2 n+1)}{3}$
  • B $\frac{2 n(n+1)(2 n+1)}{3}$
  • C $\frac{n(n+1)(2 n+1)}{6}$
  • D $\frac{n(n+1)(2 n+1)}{9}$
Solution:
2193 Upvotes Verified Answer
The correct answer is: $\frac{2 n(n+1)(2 n+1)}{3}$
$2^2+4^2+6^2+\ldots \ldots \ldots+(2 n)^2$ $=2^2\left(1^2+2^2+3^2+\ldots \ldots . .+n^2\right)$
$=\frac{4 n(n+1)(2 n+1)}{6}=\frac{2 n(n+1)(2 n+1)}{3}$

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