| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Two linear factors in denominator |
| Difficulty | Standard +0.8 This is a Further Maths (FP2) question requiring partial fractions followed by telescoping series summation with proof. Part (a) is routine, but part (b) requires recognizing the telescoping pattern, careful algebraic manipulation across multiple terms, and proving a non-trivial closed form—significantly above standard A-level but typical for Further Maths series questions. |
| Spec | 4.05c Partial fractions: extended to quadratic denominators4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\alph*)]
\item Express $\frac{1}{t(t+2)}$ in partial fractions. [1]
\item Hence show that $\sum_{n=1}^{\infty} \frac{4}{n(n+2)} = \frac{n(3n+5)}{(n+1)(n+2)}$ [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q1 [6]}}