| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Moderate -0.3 This is a straightforward proof by induction requiring standard summation formulas for Σr and Σr². While it involves algebraic manipulation across multiple steps, the technique is routine and well-practiced at A-level, with no conceptual difficulty or novel insight required. The 4 marks reflect the mechanical nature of expanding, collecting terms, and verifying the formula. |
| Spec | 4.01a Mathematical induction: construct proofs4.06a Summation formulae: sum of r, r^2, r^3 |
Prove that
$$\sum_{r=1}^{n} 18(r^2 - 4) = n(6n^2 + 9n - 69).$$
[4 marks]
\hfill \mbox{\textit{SPS SPS FM 2021 Q4 [4]}}