| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Two linear factors in denominator |
| Difficulty | Standard +0.8 This is a standard Further Maths telescoping series question requiring partial fractions decomposition followed by summation. Part (a) is routine, but part (b) requires recognizing the telescoping pattern, careful algebraic manipulation of the remaining terms, and finding a common denominator to reach the given form—more demanding than typical A-level questions but standard for FP2. |
| 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 prove that $\sum_{r=1}^{n} \frac{2}{(r + 1)(r + 3)} = \frac{n(5n + 13)}{6(n + 2)(n + 3)}$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q12 [7]}}