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KVPY2016MathematicsSequences and Series

Let S₁ be the sum of areas of the squares whose sides are parallel to coordinate axes. Let S ₂ be the sum of areas of the slanted squares as shown in the figure. Then S ₁ / S ₂ is

Options

  1. A2
  2. B2
  3. C1
  4. D1 2

Correct answer

A. 2

Step-by-step solution

S ₁= a ²+ a ² 4 + a ² 16 + = a ² 1- 1 4 = 4 a ² 3 ~S ₂= a ² 2 + a ² 8 + a ² 32 + = a ² 2 1- 1 4 = 4 a ² 6 S ₁ ~S ₂ =2

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