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JEE Main202117 Mar 2021Morning ShiftMathematicsQuadratic EquationActual

The value of 4 + 1 5 + 1 4 + 1 5 + 1 4 + … … ∞ is:

Options

  1. A2 + 2 5 30
  2. B2 + 4 5 30
  3. C4 + 4 5 30
  4. D5 + 2 5 30

Correct answer

A. 2 + 2 5 30

Step-by-step solution

Given y = 4 + 1 5 + 1 4 + 1 5 + 1 4 + … … ∞ ⏟ y y = 4 + 1 5 + 1 y ⇒ y - 4 = y ( 5 y + 1 ) ⇒ 5 y 2 - 20 y - 4 = 0 ⇒ y = 20 ± - 20 2 - 4 · 5 · - 4 2 · 5 ⇒ y = 20 ± 480 10 ∴   y = 2 - 480 100 → rejected So, y = 2 + 480 100 = 2 + 2 5 30 Correct with Option (A).

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