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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

The value of _ n → ∞ ∑_ k=1 ^n (n-k)/(n^2) (4k)/(n) equals :

The value of lim⁡n→∞∑k=1nn−kn2cos⁡4kn\lim_{n \to \infty} \sum_{k=1}^n \frac{n-k}{n^2} \cos \frac{4k}{n} equals :

Options

  1. A14sin⁡4+116cos⁡4−116\frac{1}{4} \sin 4 + \frac{1}{16} \cos 4 - \frac{1}{16}
  2. B14sin⁡4−116cos⁡4+116\frac{1}{4} \sin 4 - \frac{1}{16} \cos 4 + \frac{1}{16}
  3. C116(1−sin⁡4)\frac{1}{16}(1 - \sin 4)
  4. D116(1−cos⁡4)\frac{1}{16}(1 - \cos 4)

Correct answer

D. 116(1−cos⁡4)\frac{1}{16}(1 - \cos 4)

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