| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Moderate -0.5 This is a standard proof by induction with a straightforward algebraic manipulation. While it's Further Maths content, the inductive step requires only basic factorization of a cubic expression, making it easier than average even for FP1. The formula and structure are typical textbook fare with no novel insight required. |
| Spec | 4.01a Mathematical induction: construct proofs |
Prove by induction that, for $n \geq 1$, $\sum_{r=1}^{n} r(r + 1) = \frac{1}{3}n(n + 1)(n + 2)$. [5]
\hfill \mbox{\textit{OCR FP1 2010 Q1 [5]}}