| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Moderate -0.3 This is a straightforward proof by induction of a summation formula. While it's Further Maths content, the technique is standard: verify base case, assume for n=k, prove for n=k+1. The algebra is routine (expanding and factoring cubics), requiring no novel insight—just careful execution of a well-practiced method. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
Prove that
$$\sum_{r=1}^{n} 6(r^2 - 1) = (n - 1)n(2n + 5).$$
[4]
\hfill \mbox{\textit{Edexcel FP1 Q5 [4]}}