| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove summation formula |
| Difficulty | Moderate -0.5 This is a standard textbook induction proof of a well-known summation formula. While it requires understanding of the induction framework and algebraic manipulation to verify the inductive step, it follows a completely routine template with no novel insight required. The algebra is straightforward compared to more complex induction proofs, making it slightly easier than average but still requiring proper technique. |
| Spec | 4.01a Mathematical induction: construct proofs |
Prove by induction that $\sum_{r=1}^{n} r^2 = \frac{1}{6}n(n+1)(2n+1)$. [8]6 Prove by induction that $\sum _ { r = 1 } ^ { n } r ^ { 2 } = \frac { 1 } { 6 } n ( n + 1 ) ( 2 n + 1 )$.
\hfill \mbox{\textit{OCR MEI FP1 2007 Q6 [8]}}