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JEE Main2002MathematicsDefinite IntegrationActual

I_n= ₀^ / 4 ^n x d x then Lim _ n n [I_n+I_ n-2 ] equals

Options

  1. A1/2
  2. B1
  3. Czero

Correct answer

B. 1

Step-by-step solution

₀^ / 4 ^n x (1+ ^2 x ) d x= ₀^ / 4 ^n x ^2 x d x= ₀^1 t^n d t where t= xI_n+I_ n+2 = 1 n+1 ; Lim _ x n [l_n+I_ n+2 ]= Lim _ x n 1 n+1 = n n+1 = n n (1+ 1 n ) =1

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