| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Standard +0.3 This is a standard proof by induction question with straightforward algebra. The summation expands to a cubic expression, and the inductive step requires routine algebraic manipulation. While it's a 6-mark question requiring careful working, it follows a completely standard template that Further Maths students practice extensively, making it slightly easier than average. |
| Spec | 1.04g Sigma notation: for sums of series4.01a Mathematical induction: construct proofs |
Prove that $\sum_{r=1}^{n} (r - 1)(r + 2) = \frac{1}{3} (n - 1)n(n + 4)$.
[6]
\hfill \mbox{\textit{Edexcel FP1 Q27 [6]}}