| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 6 |
| 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 straightforward method of differences question requiring algebraic manipulation to verify the given identity, then telescoping sum application. The factorial manipulation in part (i) is routine, and part (ii) follows directly by recognizing the telescoping pattern. Slightly easier than average as it's a standard FP1 technique with clear signposting. |
| Spec | 4.01a Mathematical induction: construct proofs4.06b Method of differences: telescoping series |
3 (i) Show that $\frac { 1 } { r ! } - \frac { 1 } { ( r + 1 ) ! } = \frac { r } { ( r + 1 ) ! }$.\\
(ii) Hence find an expression, in terms of $n$, for
$$\frac { 1 } { 2 ! } + \frac { 2 } { 3 ! } + \frac { 3 } { 4 ! } + \ldots + \frac { n } { ( n + 1 ) ! }$$
\hfill \mbox{\textit{OCR FP1 2008 Q3 [6]}}