| Exam Board | AQA |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2013 |
| Session | January |
| 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 FP2 method of differences question with routine partial fractions. Part (a) is algebraic verification, part (b) follows a well-practiced telescoping technique, and part (c) is a direct limit. While it's Further Maths content, the execution is mechanical with no novel insight required, making it slightly easier than average overall. |
| Spec | 4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\alph*)]
\item Show that $\frac{1}{5r-2} - \frac{1}{5r+3} = \frac{A}{(5r-2)(5r+3)}$, stating the value of the constant $A$. [2 marks]
\item Hence use the method of differences to show that
$$\sum_{r=1}^{n} \frac{1}{(5r-2)(5r+3)} = \frac{n}{3(5n+3)}$$ [4 marks]
\item Find the value of
$$\sum_{r=1}^{\infty} \frac{1}{(5r-2)(5r+3)}$$ [1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA FP2 2013 Q3 [7]}}