| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Method of differences with given identity |
| Difficulty | Moderate -0.8 Part (i) is trivial algebraic verification requiring only finding a common denominator. Part (ii) is a standard textbook application of the method of differences with telescoping series—a routine FP1 technique with no problem-solving required. The calculation is straightforward once the pattern is recognized, making this significantly easier than average A-level questions. |
| Spec | 4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\roman*)]
\item Show that $\frac{1}{r+2} - \frac{1}{r+3} = \frac{1}{(r+2)(r+3)}$. [2]
\item Hence use the method of differences to find $\frac{1}{3 \times 4} + \frac{1}{4 \times 5} + \frac{1}{5 \times 6} + \ldots + \frac{1}{52 \times 53}$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI FP1 2007 Q6 [6]}}