| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 7 |
| 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 partial fractions question with method of differences. While it requires multiple techniques (partial fractions, telescoping series, substitution), these are routine FP2 procedures with no novel insight needed. The algebraic manipulation is straightforward and the question structure is highly typical of textbook exercises. |
| Spec | 4.05c Partial fractions: extended to quadratic denominators4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\alph*)]
\item Express $\frac{3}{(3r-1)(3r+2)}$ in partial fractions. [2]
\item Using your answer to part (a) and the method of differences, show that
$$\sum_{r=1}^n \frac{3}{(3r-1)(3r+2)} = \frac{3n}{2(3n+2)}$$ [3]
\item Evaluate $\sum_{r=1}^{30} \frac{3}{(3r-1)(3r+2)}$, giving your answer to 3 significant figures. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q1 [7]}}