Find the sum of the series `2^2+4^2+6^2++(2n)^2`

1.	Find the sum of the series `2^2+4^2+6^2++(2n)^2`
Answer» Correct Answer - `(2)/(3)n(n+1)(2n+1)` `T_(k)=(2k)^(2)=4k^(2).` `therefore S_(n)=sum_(k=1)^(n)T_(k)=4(sum_(k=1)^(n)k^(2))={4xx(1)/(6)n(n+1)(2n+1)}=(2)/(3)n(n+1)(2n+1)`.

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