| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2023 |
| Session | February |
| Marks | 4 |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Moderate -0.8 This is a straightforward application of standard summation formulas requiring substitution of Σr² = n(n+1)(2n+1)/6 and Σ1 = n, followed by algebraic simplification and factorisation. It's routine bookwork with no problem-solving element, making it easier than average but not trivial since it requires correct manipulation and factorisation of the resulting expression. |
| Spec | 1.04g Sigma notation: for sums of series4.06a Summation formulae: sum of r, r^2, r^3 |
Find $\sum_{r=1}^{n}(2r^2 - 1)$, expressing your answer in fully factorised form.
[4]
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q1 [4]}}