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The product 2 1 4 ∙ 4 1 16 ∙ 8 1 48 ∙ 16 1 128 ∙ . . . . to ∞ is equal to:

Options

  1. A2 1 2
  2. B2 1 4
  3. C1
  4. D2

Correct answer

A. 2 1 2

Step-by-step solution

2 1 4 + 2 16 + 3 48 + … … … . ∞ S = 2 1 4 + 1 8 + 1 16 + … . . ∞     . . . . i ∴ 1 4 + 1 8 + 1 16 + . . . ∞ is an infinite G.P with a = 1 4 ,   r = 1 2 S ∞ = a 1 - r = 1 2 Using equation i , S = 2

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