Answer: 1/4 - 1/(2(n+1)(n+2)).
- A 1/4 - 1/(2(n+1)(n+2))
- B 1/4, without the correction term for finite n
- C 1/2(n+1), a partial telescoping result
- D n/(n+1)(n+2), a related but different ratio
Correct answer: A. 1/4 - 1/(2(n+1)(n+2))
Explanation: Using partial fractions: each term = 1/2 [1/(k(k+1)) - 1/((k+1)(k+2))]. Telescoping: 1/2 [1/(1×2) - 1/((n+1)(n+2))] = 1/4 - 1/(2(n+1)(n+2)).
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