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📐 Mathematics  ·  Sequences and Series  ·  JEE

Telescoping sum: sum from k=1 to n of [1/k - 1/(k+1)] =

Answer: n/(n+1).

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

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

Explanation: Telescoping: terms cancel in pairs. (1−½)+(½−⅓)+…+(1/n−1/(n+1)) = 1 − 1/(n+1) = n/(n+1). All middle terms vanish.

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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