Answer: n(n+1)(n+2)/3.
- A n(n+1)(n+2)/3
- B n(n+1)/2
- C n²(n+1)²/4
- D n(n+1)(2n+1)/6
Correct answer: A. n(n+1)(n+2)/3
Explanation: Σk(k+1) = Σk² + Σk = n(n+1)(2n+1)/6 + n(n+1)/2. Factor n(n+1): n(n+1)[(2n+1)/6 + 3/6] = n(n+1)(2n+4)/6 = n(n+1)(n+2)/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