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If is the complex cube root of unity, then the value of + ^ ( 1 2 + 3 8 + 9 32 + 27 128 + ) is

Options

  1. A-1
  2. B1
  3. C- i
  4. Di

Correct answer

A. -1

Step-by-step solution

Consider 1 2 + 3 8 + 9 32 + 27 128 + . Which can be written as 3⁰ 2¹ + 3¹ 2³ + 3² 2⁵ + 3³ 2⁷ + . = 1 2 [1+ 3 2² + 3² 2⁴ + 3³ 2⁶ + . ] Since (1+ 3 2² + 3² 2⁴ +_ -- - ) is a G.P. therfore by sum of infinite G.P, we have = 1 2 [ 1 1- 3 2² ]= 1 2 [ 1 1- 3 4 ]=2 Given expression array l =-1 [ 1+ + ²=0 ] array

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