| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Method of differences with given identity |
| Difficulty | Standard +0.3 This is a standard telescoping series question with clear scaffolding. Part (i) is routine algebraic verification (2 marks). Part (ii) applies the given result to sum a series by telescoping—a technique explicitly taught in FP1. Part (iii) is immediate once part (ii) is complete. While it requires understanding of series and limits, the question structure guides students through each step, making it easier than average for an A-level question, though appropriately challenging for FP1 content. |
| Spec | 4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\roman*)]
\item Show that
$$\frac{r+1}{r+2} - \frac{r}{r+1} = \frac{1}{(r+1)(r+2)}.$$ [2]
\item Hence find an expression, in terms of $n$, for
$$\frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \ldots + \frac{1}{(n+1)(n+2)}.$$ [4]
\item Hence write down the value of $\sum_{r=1}^\infty \frac{1}{(r+1)(r+2)}$. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 Q5 [7]}}