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The value of _ r=1 ^ [3 2^ -r -2 3^ 1-r ] is

Options

  1. A2
  2. B1 / 2
  3. C1
  4. D0

Correct answer

D. 0

Step-by-step solution

_ r=1 ^ [3 2^ -r -2 3^ 1-r ]=3 _ r=1 ^ 1 2^r -2 _ r=1 ^n 3^ 1-r aligned & =3 [ 1 2 + 1 2^2 + ]-2 [1+ 1 3 + 1 3^2 + ] & = 3 2 [1+ 1 2 + 1 2^2 + ]-2 [1+ 1 3 + 1 3^2 + ] & = 3 2 ( 1 1- 1 2 )-2 ( 1 1- 1 3 )= 3 2 2- 2 3 2 =0 aligned

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