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📐 Mathematics  ·  Sequences and Series  ·  JEE

The sum 1/(1×2) + 1/(2×3) + 1/(3×4) + ... to n terms =

Answer: n/(n+1).

  • A n/(n+1)
  • B 1/(n+1)
  • C n(n+2)
  • D 1/n

Correct answer: A. n/(n+1)

Explanation: Each term 1/(k(k+1)) = 1/k - 1/(k+1) (partial fractions). Sum telescopes to 1 - 1/(n+1) = n/(n+1).

Each bar grows by the common difference d=3a1=2a2=5a3=8a4=11d=3

Bar heights for AP 2, 5, 8, 11 with the common difference d=3 marked between consecutive terms.

Concept context

Arithmetic progressions, geometric progressions, and sums

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