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JEE Main20236 Apr 2023Evening ShiftMathematicsLimitsActual

lim n → ∞ 2 1 2 - 2 1 3 2 1 2 - 2 1 5 . . . . 2 1 2 - 2 1 2 n + 1 is equal to

Options

  1. A1
  2. B0
  3. C2
  4. D1 2

Correct answer

B. 0

Step-by-step solution

Let, L = lim n → ∞ 2 1 2 - 2 1 3 2 1 2 - 2 1 5 . . . . 2 1 2 - 2 1 2 n + 1 Now, 2 1 2 - 2 1 3 < 1 2 1 2 - 2 1 5 < 1 -------------------- 2 1 2 - 2 1 2 n + 1 < 1       ∀ n ∈ N And 2 1 2 - 2 1 3 n < 2 1 2 - 2 1 3 2 1 2 - 2 1 5 . . . . 2 1 2 - 2 1 2 n + 1 < 2 1 2 - 2 1 2 n + 1 n ⇒ lim n → ∞ 2 1 2 - 2 1 3 n < lim n → ∞ 2 1 2 - 2 1 3 2 1 2 - 2 1 5 . . . . 2 1 2 - 2 1 2 n + 1 < lim n → ∞ 2 1 2 - 2 1 2 n + 1 n &#86

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