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Question 210025
JEE Mathematics · Hard

Sequences and Series: Telescoping MCQ

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TelescopingHardQuestion 210025

Question

The sum Σ(r=1 to n) 1/(r(r+1)) equals:
  1. A
    n/(n+1)
    Correct
  2. B
    1/(n+1)
  3. C
    (n+1)/n
  4. D
    1/n

Correct answer

n/(n+1)

Explanation

Partial fractions: 1/(r(r+1)) = 1/r − 1/(r+1). Telescoping: (1 − 1/2) + (1/2 − 1/3) + ... + (1/n − 1/(n+1)) = 1 − 1/(n+1) = n/(n+1).

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