| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 3 |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Standard +0.8 This requires expanding n(n+1)² into polynomial terms, applying three standard summation formulae (Σn³, Σn², Σn), then algebraically simplifying and factorising the result. While methodical, it demands careful algebraic manipulation across multiple steps and is more demanding than typical A-level questions, placing it moderately above average difficulty. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
1 Find an expression for $1 \times 2 ^ { 2 } + 2 \times 3 ^ { 2 } + 3 \times 4 ^ { 2 } + \ldots + n ( n + 1 ) ^ { 2 }$ in terms of $n$. Give your answer in fully factorised form.
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q1 [3]}}