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If G is the geometric mean of numbers 1,2,2^2, 2^3, , 2 n⁻¹ , then what is the value of 1+2 ₂ G ?

Options

  1. A1
  2. B4
  3. Cn-1
  4. Dn

Correct answer

D. n

Step-by-step solution

1,2,2^2, 2^3, . .2 n⁻¹ Number of terms =n GM = (1 2 2^2 2^3 2^ n-1 )^ 1 / n = (2^ 1+2+3+ +(n-1) )^ 1 / n = [2^ n(n-1) 2 ]^ 1 / n G=2^ n-1 2 1+2 ₂ G=1+2 ₂ 2^ n-1 2 =1+2 (n-1) 2 ₂ 2=1+n-1=n

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