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KVPY2011MathematicsLimits

The value of _ n ( 1 4 n²-1 + 1 4 n²-4 + + 1 4 n²-n² ) is -

Options

  1. A1 4
  2. B12
  3. C4
  4. D6

Correct answer

D. 6

Step-by-step solution

_ n _ r=1 ^ n 1 4 n²-r² = _ n 1 n _ r=1 ^ n 1 4-(r / n)² = ₀¹ d x 4-x² = ( ⁻¹ ( x 2 ) )₀¹= 6

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