| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Sum from n+1 to 2n or similar range |
| Difficulty | Standard +0.3 This is a standard Further Maths method of differences question with routine partial fractions. Part (a) is straightforward A-level algebra, part (b) follows a well-practiced telescoping technique, and part (c) is simple substitution. While it's FP2 content, it requires no novel insight—just methodical application of textbook methods, making it slightly easier than average overall. |
| Spec | 1.02y Partial fractions: decompose rational functions4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\alph*)]
\item Express $\frac{1}{r(r + 2)}$ in partial fractions. [2]
\item Hence prove, by the method of differences, that
$$\sum_{r=1}^{n} \frac{4}{r(r + 2)} = \frac{n(3n + 5)}{(n + 1)(n + 2)}.$$ [5]
\item Find the value of $\sum_{r=50}^{100} \frac{4}{r(r + 2)}$, to 4 decimal places. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q38 [10]}}