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The sum of the first \(n\) terms of the sequence \(\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\ldots\) is

Question and options

The sum of the first nn terms of the sequence 11×2+12×3+13×4+…\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\ldots is
  1. 1n+1\frac{1}{n+1}
  2. 1n\frac{1}{n}
  3. n+1n\frac{n+1}{n}
  4. nn+1\frac{n}{n+1}

Answer and explanation

Correct answer: D - \(\frac{n}{n+1}\)
1/(k(k+1)) = 1/k - 1/(k+1). The sum telescopes to 1 - 1/(n+1) = n/(n+1).

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