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The sequence a_n is defined by a₁= 1 2 , a_ n+1 =a_n^2+a_n . Also, s= 1 a₁+1 + 1 a₂+1 + . .+ 1 a₁₀₀+1 then [ S ] (where [.] denotes the greatest integer function) is

Options

  1. A1
  2. B2
  3. C3
  4. Dnone of these

Correct answer

A. 1

Step-by-step solution

1 a_ n+1 = 1 a_n (a_n+1 ) = 1 a_n - 1 a_n+1 S= 1 a₁ - 1 a₂ + . .+ 1 a₁₀₀ - 1 a₁₀₁ = 1 a₁ - 1 a₁₀₁ =2- 1 a₁₀₁ Since, a₁₀₁ 1 [S]=1

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