| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2005 |
| Session | January |
| 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 -0.5 This is a straightforward application of the method of differences with the identity explicitly provided. Part (i) is trivial algebra (common denominator), and part (ii) requires only mechanical telescoping of the given form. While method of differences is a Further Maths topic, the question involves no problem-solving or insight since the decomposition is given, making it easier than average overall. |
| Spec | 4.06b Method of differences: telescoping series |
2 (i) Show that $\frac { 1 } { r + 1 } - \frac { 1 } { r + 2 } = \frac { 1 } { ( r + 1 ) ( r + 2 ) }$.\\
(ii) Hence use the method of differences to find the sum of the series
$$\sum _ { r = 1 } ^ { n } \frac { 1 } { ( r + 1 ) ( r + 2 ) }$$
\hfill \mbox{\textit{OCR MEI FP1 2005 Q2 [6]}}