| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Partial fractions then method of differences |
| Difficulty | Moderate -0.3 This is a standard telescoping series question requiring routine partial fractions followed by recognizing cancellation patterns. Part (a) is straightforward A-level algebra, and part (b) is a textbook application of telescoping sums. While it requires multiple steps (5 marks total), the techniques are well-practiced and no novel insight is needed, making it slightly easier than average. |
| Spec | 4.05c Partial fractions: extended to quadratic denominators4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\alph*)]
\item Express $\frac{2}{(2r + 1)(2r + 3)}$ in partial fractions. [2]
\item Using your answer to (a), find, in terms of $n$,
$$\sum_{r=1}^n \frac{2}{(2r + 1)(2r + 3)}$$ [3]
\end{enumerate}
Give your answer as a single fraction in its simplest form.
\hfill \mbox{\textit{Edexcel FP2 Q1 [5]}}