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AP EAMCET202021 Sep 2020Morning ShiftMathematicsSequences and SeriesActual

( _ n 2^2+4^2+6^2+ +(2 n)^2 n^3 = )

Options

  1. A( 2 3 )
  2. B( 4 3 )
  3. C( 3 2 )
  4. D( 8 7 )

Correct answer

B. ( 4 3 )

Step-by-step solution

( aligned & _ n 2^2+4^2+6^2+ +(2 n)^2 n^3 & =4 _ n 1^2+2^2+3^2+ +n^2 n^3 & =4 _ n n(n+1)(2 n+1) 6 n^3 =4 _ n 1 (1+ 1 n ) (2+ 1 n ) 6 & =4 2 6 = 4 3 aligned ) Hence, option (b) is correct.

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