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JEE Main202118 Mar 2021Morning ShiftMathematicsQuadratic EquationActual

The value of 3 + 1 4 + 1 3 + 1 4 + 1 3 + … ∞ is equal to

Options

  1. A1 . 5 + 3
  2. B2 + 3
  3. C3 + 2 3
  4. D4 + 3

Correct answer

A. 1 . 5 + 3

Step-by-step solution

Let x = 3 + 1 4 + 1 3 + 1 4 + 1 3 + … ∞ So, x = 3 + 1 4 + 1 x = 3 + 1 4 x + 1 x ⇒ x - 3 = x ( 4 x + 1 ) ⇒ ( 4 x + 1 ) ( x - 3 ) = x ⇒ 4 x 2 - 12 x + x - 3 = x ⇒ 4 x 2 - 12 x - 3 = 0 x = 12 ± ( 12 ) 2 + 12 × 4 2 × 4 = 12 ± 12 ( 16 ) 8 = 12 ± 4 × 2 3 8 = 3 ± 2 3 2 x = 3 2 ± 3 = 1 . 5 ± 3 . But only positive value is accepted So, x = 1 . 5 + 3

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