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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 → ∞ ( 1 n n+1 + 1 n n+2 + 1 n n+3 + + 1 n 2n )...

The value of : $\lim_{n \to \infty} \left( \frac{1}{\sqrt{n}\sqrt{n+1}} + \frac{1}{\sqrt{n}\sqrt{n+2}} + \frac{1}{\sqrt{n}\sqrt{n+3}} + \dots + \frac{1}{\sqrt{n}\sqrt{2n}} \right) is :

Options

  1. A2−1\sqrt{2} - 1
  2. B2(2−1)2(\sqrt{2} - 1)
  3. C2+1\sqrt{2} + 1
  4. D2(2+1)2(\sqrt{2} + 1)

Correct answer

B. 2(2−1)2(\sqrt{2} - 1)

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