| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Partial fractions then method of differences |
| Difficulty | Standard +0.3 This is a standard Further Maths telescoping series question with routine partial fractions decomposition followed by algebraic manipulation. While it requires multiple steps and careful bookkeeping, the techniques are well-practiced and the question follows a familiar template with no novel insights required, 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 $\frac{2}{(r + 1)(r + 3)}$ in partial fractions. [2]
\item Hence show that
$$\sum_{r=1}^{\infty} \frac{2}{(r + 1)(r + 3)} = \frac{n(5n + 13)}{6(n + 2)(n + 3)}$$ [4]
\item Evaluate $\sum_{r=1}^{30} \frac{2}{(r + 1)(r + 3)}$, giving your answer to 3 significant figures. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q3 [8]}}