| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795 (Pre-U Further Mathematics) |
| Session | Specimen |
| Marks | 6 |
| Topic | Sequences and series, recurrence and convergence |
| Type | Alternating series summation |
| Difficulty | Standard +0.3 This question requires knowing the standard sum formula for cubes and then using algebraic manipulation to separate odd and even terms. While it involves multiple steps, the techniques are straightforward: recall a standard result, split the alternating sum into two parts, and simplify. The algebraic manipulation is routine for Further Maths students, making this slightly easier than average. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^34.06b Method of differences: telescoping series |
Write down the sum
$$\sum_{n=1}^{2N} n^3$$
in terms of $N$, and hence find
$$1^3 - 2^3 + 3^3 - 4^3 + \ldots - (2N)^3$$
in terms of $N$, simplifying your answer. [6]
\hfill \mbox{\textit{Pre-U Pre-U 9795 Q4 [6]}}