| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Limit of ratio of sums |
| Difficulty | Standard +0.8 This requires knowing or deriving formulas for sum of squares (n(n+1)(2n+1)/6) and sum of integers (n(n+1)/2), simplifying the ratio to (2n+1)/3, then solving an inequality. It's a multi-step problem requiring formula recall and algebraic manipulation, moderately harder than average but standard for Further Maths. |
| Spec | 4.01a Mathematical induction: construct proofs4.06a Summation formulae: sum of r, r^2, r^3 |
4 In this question you must show detailed reasoning.\\
Determine the smallest value of $n$ for which $\frac { 1 ^ { 2 } + 2 ^ { 2 } + \ldots + n ^ { 2 } } { 1 + 2 + \ldots + n } > 341$.
\hfill \mbox{\textit{OCR Further Pure Core 2 2022 Q4 [4]}}