| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Standard +0.3 This is a straightforward summation question requiring expansion of the product, application of standard summation formulas (Σr and Σr²), and algebraic manipulation to reach the given result. Part (b) is routine substitution. While it requires careful algebra, it's a standard FP1 exercise with no novel insight needed—slightly easier than average A-level difficulty. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^34.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\alph*)]
\item Show that $\sum_{r=1}^{n} (r + 1)(r + 5) = \frac{1}{6} n(n + 7)(2n + 7)$. [4]
\item Hence calculate the value of $\sum_{r=10}^{40} (r + 1)(r + 5)$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q16 [6]}}