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What is the greatest value of the positive integer n satisfying the condition 1+ 1 2 + 1 4 + 1 8 + . .+ 1 2^ n -1 2- 1 1000 ?

Options

  1. A8
  2. B9
  3. C10
  4. D11

Correct answer

C. 10

Step-by-step solution

1+ 1 2 + 1 4 + 1 8 + + 1 2^ n-1 2- 1 1000 LHS of given inequality is in G.P. aligned & 1- 1 2^ n 1- 1 2 2- 1 1000 & 2- 1 2^ n -1 2- 1 1000 & 2^ n -1 1000 aligned aligned & Now, (2)^9=512 &(2)¹⁰=1024 & n -1=9 & n =10 . aligned

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