| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Proving standard summation formulae |
| Difficulty | Challenging +1.2 This is a standard Further Maths proof technique requiring students to find an appropriate expression f(r) whose differences telescope to r². While it requires more sophistication than basic C1/C2 work (finding that f(r) = r(r+1)(2r+1)/6 works), it's a well-practiced method in FP2 with a clear algorithmic approach. The 6 marks reflect multiple steps but no novel insight is needed. |
| Spec | 4.06b Method of differences: telescoping series |
Prove by the method of differences that $\sum_{r=1}^{n} r^2 = \frac{1}{6}n(n + 1)(2n + 1)$, $n > 1$.
[6]
\hfill \mbox{\textit{Edexcel FP2 Q24 [6]}}