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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

_ n → ∞ (1)/(n^3) ( n^2+1 + 2 n^2+2^2 + + n n^2+n^2 ) = :

lim⁡n→∞1n3(n2+1+2n2+22+⋯+nn2+n2)=\lim_{n \to \infty} \frac{1}{n^3} \left( \sqrt{n^2+1} + 2\sqrt{n^2+2^2} + \dots + n\sqrt{n^2+n^2} \right) = :

Options

  1. A32−12\frac{3\sqrt{2}-1}{2}
  2. B22−13\frac{2\sqrt{2}-1}{3}
  3. C33−13\frac{3\sqrt{3}-1}{3}
  4. D42−12\frac{4\sqrt{2}-1}{2}

Correct answer

B. 22−13\frac{2\sqrt{2}-1}{3}

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