| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Finding constants from given sum formula |
| Difficulty | Standard +0.3 This is a straightforward algebraic manipulation question requiring expansion of the sum, application of two standard formula results (∑r and ∑r³), factorization, and comparison of coefficients. While it involves multiple steps and is from Further Maths F1, the techniques are routine and the path is clear, making it slightly easier than average overall but typical for Further Pure. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
\begin{enumerate}
\item Use the standard results for $\sum _ { r = 1 } ^ { n } r$ and for $\sum _ { r = 1 } ^ { n } r ^ { 3 }$ to show that, for all positive integers $n$,
\end{enumerate}
$$\sum _ { r = 1 } ^ { n } r \left( r ^ { 2 } - 3 \right) = \frac { n } { 4 } ( n + a ) ( n + b ) ( n + c )$$
where $a$, $b$ and $c$ are integers to be found.
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\hfill \mbox{\textit{Edexcel F1 2016 Q1 [4]}}