AS October 2021 Paper 1 Q1
1 Using standard summation formulae, find \(\displaystyle\sum_{r=1}^{n}(r^2 - 3r)\), giving your answer in fully factorised form. [3]
| Scheme | Marks | AO |
|---|---|---|
| \(\displaystyle\sum_{r=1}^{n}(r^2 - 3r) = \sum_{r=1}^{n}r^2 - 3\sum_{r=1}^{n}r\) | M1 | 1.1a |
| \(= \tfrac{1}{6}n(n + 1)(2n + 1) - \tfrac{3}{2}n(n + 1)\) | A1 | 1.1 |
| \(= \tfrac{1}{3}n(n + 1)(n - 4)\) | A1 | 1.1 |
| [3] |