| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Finding constants from given sum formula |
| Difficulty | Moderate -0.5 This is a straightforward algebraic manipulation question requiring expansion of r(r+3), application of two standard summation formulas, factorization, and comparison of coefficients. While it involves Further Maths content, it's a routine exercise with clear steps and no conceptual challenges beyond formula recall and basic algebra. |
| Spec | 1.04g Sigma notation: for sums of series4.06a Summation formulae: sum of r, r^2, r^3 |
\begin{enumerate}
\item Use the standard results for $\sum _ { r = 1 } ^ { n } r$ and for $\sum _ { r = 1 } ^ { n } r ^ { 2 }$ to show that, for all positive integers $n$,
\end{enumerate}
$$\sum _ { r = 1 } ^ { n } r ( r + 3 ) = \frac { n } { a } ( n + 1 ) ( n + b )$$
where $a$ and $b$ are integers to be found.\\
\hfill \mbox{\textit{Edexcel F1 2018 Q1 [4]}}