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The value of 1 ₃ e + 1 ₃ e^2 + 1 ₃ e^4 + . up to infinite terms is

Options

  1. A_e 9
  2. B0
  3. C1
  4. D_e 3

Correct answer

A. _e 9

Step-by-step solution

1 ₃ e + 1 ₃ e ^2 + 1 ₃ e ^4 + = 1 ₃ e + 1 2 ₃ e + 1 4 ₃ e + ( . Since, . _ a b ^ m = m log _ a b )= _ e 3+ _ e 3 2 + _ e 3 4 + . ( . Since, . _ a b = 1 _ b a )= _ e 3 (1+ 1 2 + 1 4 + . )= _ e 3 ( 1 1- 1 2 ) ( 1, 1 2 , 1 4 . is G.P. with . a =1, r = 1 2 )= _ e 3(2)=2 _ e 3= _ e 3^2= _ e 9 .

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