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If H is the harmonic mean of numbers 1,2.2^2, 2^3, , 2 n⁻¹ , then what is n / H equal to?

Options

  1. A2- 1 2^ n+1
  2. B2- 1 2^ n-1
  3. C2+ 1 2^ n-1
  4. D2- 1 2^n

Correct answer

B. 2- 1 2^ n-1

Step-by-step solution

n 1 a₁ + 1 a₂ + + 1 a_n =H n H = 1 a₁ + 1 a₂ + + 1 a_n =1+ 1 2 + 1 2^2 + + 1 2^ n-1 = 1 ( ( 1 2 )^n-1 ) ( 1 2 -1 ) =2 (1- 1 2^n ) n H =2- 1 2^ n-1

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