| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Method of differences with given identity |
| Difficulty | Standard +0.8 This is a Further Maths FP2 question requiring students to verify a given telescoping identity, then apply method of differences to sum a series. While the identity is provided in part (a), students must recognize how to manipulate the general term algebraically to match the telescoping form, then execute the telescoping sum correctly. This requires more sophistication than standard A-level series questions but is a fairly standard FP2 technique once learned. |
| Spec | 4.06b Method of differences: telescoping series |
\begin{enumerate}
\item (a) Express as a simplified single fraction $\frac { 1 } { r ^ { 2 } } - \frac { 1 } { ( r + 1 ) ^ { 2 } }$\\
(b) Hence prove, by the method of differences, that
\end{enumerate}
$$\sum _ { r = 1 } ^ { n } \frac { 2 r + 1 } { r ^ { 2 } ( r + 1 ) ^ { 2 } } = 1 - \frac { 1 } { ( n + 1 ) ^ { 2 } }$$
\hfill \mbox{\textit{Edexcel FP2 Q2 [5]}}