| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Sum from n+1 to 2n or similar range |
| Difficulty | Standard +0.3 This is a straightforward application of standard summation formulas. Part (a) requires algebraic manipulation of known results for Σr² and Σr, which is routine for Further Maths students. Part (b) is a direct application of the formula from part (a) using difference of sums. No novel insight required, just careful algebraic execution. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
\begin{enumerate}
\item (a) Use the standard results for $\sum _ { r = 1 } ^ { n } r ^ { 2 }$ and $\sum _ { r = 1 } ^ { n } r$ to show that for all positive integers $n$
\end{enumerate}
$$\sum _ { r = 0 } ^ { n } ( r + 1 ) ( r + 2 ) = \frac { 1 } { 3 } ( n + 1 ) ( n + 2 ) ( n + 3 )$$
(b) Hence determine the value of
$$10 \times 11 + 11 \times 12 + 12 \times 13 + \ldots + 100 \times 101$$
\hfill \mbox{\textit{Edexcel F1 2022 Q8 [8]}}