| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Moderate -0.3 Part (a) is a straightforward application of standard summation formulae requiring algebraic manipulation to verify a given result—routine for FP1 students. Part (b) appears to have a typo (likely asking for a specific n or different sum), but even interpreting generously, this is a standard textbook exercise testing formula recall and algebraic verification rather than problem-solving or novel insight. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
\begin{enumerate}[label=(\alph*)]
\item Show, using the formulae for $\sum r$ and $\sum r^2$, that
$$\sum_{r=1}^n (6r^2 + 4r - 1) = n(n + 2)(2n + 1).$$
[5]
\item Hence, or otherwise, find the value of $\sum_{r=1}^n (6r^2 + 4r - 1)$.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q2 [7]}}