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The value of the infinite product 6^ 1 2 6^ 1 2 6^ 3 8 6^ 1 4 is

Options

  1. A6
  2. B36
  3. C216

Correct answer

B. 36

Step-by-step solution

aligned & X=6^ 1 / 2 6^ 1 / 2 6^ 3 / 8 6^ 4 / 16 & =6^ ( 1 2 + 2 4 + 3 8 + ) & Let S= 1 2 + 2 4 + 3 8 + 4 16 + & 1 2 S=+ 1 4 + 2 8 + 3 16 + & (1- 1 2 ) S= 1 2 + (2-1) 4 + (3-2) 8 + (4-3) 16 + & S 2 = 1 2 + 1 4 + 1 8 + 1 16 + & S 2 = 1 2 1- 1 2 =1 . & S=2 x=6^2=36 aligned

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