| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Factorial or product method of differences |
| Difficulty | Standard +0.3 This is a standard FP1 summation question testing method of differences and verification using standard formulae. Part (i) is straightforward algebra, part (ii) is a textbook application of differences (though worth 6 marks for showing telescoping), and part (iii) is routine substitution. While it requires multiple techniques, all are well-practiced FP1 methods with no novel insight needed, making it slightly easier than average overall. |
| Spec | 4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\roman*)]
\item Show that $r(r+1)(r+2) - (r-1)r(r+1) \equiv 3r(r+1)$. [2]
\item Hence use the method of differences to find an expression for $\sum_{r=1}^{n} r(r+1)$. [6]
\item Show that you can obtain the same expression for $\sum_{r=1}^{n} r(r+1)$ using the standard formulae for $\sum_{r=1}^{n} r$ and $\sum_{r=1}^{n} r^2$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI FP1 2006 Q9 [13]}}