| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Method of differences with given identity |
| Difficulty | Standard +0.8 This is a Further Maths FP2 question on method of differences requiring algebraic manipulation to express the summand in telescoping form, then careful tracking of terms. Part (a) is straightforward algebra (2 marks), but part (b) requires recognizing how to use part (a) to prove the sum formula via telescoping—a technique that requires insight beyond routine application. The multi-step proof and need to connect parts (a) and (b) places this moderately above average difficulty. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\alph*)]
\item Express as a simplified fraction $\frac{1}{(r-1)^2} - \frac{1}{r^2}$. [2]
\item Prove, by the method of differences, that
$$\sum_{r=2}^{n} \frac{2r-1}{r^2(r-1)^2} = 1 - \frac{1}{n^2}.$$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q17 [5]}}