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KVPY2017MathematicsDefinite Integration

Let a_ n = _ - ^ |x-1| n x d x for all natural numbers n . Then the sequence (a_ n )_ n 0 satisfies

Options

  1. A_ n a_ n =
  2. B_ n a_ n =-
  3. C_ n a_ n exists and is positive
  4. D_ n a_ n =0

Correct answer

D. _ n a_ n =0

Step-by-step solution

a_ n = _ - ¹-(x-1) n x d x+ ₁^ (x-1) n x d x Solve I & II part by I LATE a_ n =2 n n + 2 n ² n - 2 n ² n _ x a_ n =0

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