| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Sequences and series, recurrence and convergence |
| Type | Infinite series convergence and sum |
| Difficulty | Standard +0.3 This is a standard Further Maths telescoping series question requiring partial fractions decomposition and recognizing cancellation patterns. While it involves multiple steps (factorizing, partial fractions, telescoping sum, limit), these are well-practiced techniques in FP2 with no novel insight required. The algebraic manipulation is routine for Further Maths students, making it slightly easier than average. |
| Spec | 1.02y Partial fractions: decompose rational functions4.06b Method of differences: telescoping series |
2 In this question you must show detailed reasoning.
\begin{enumerate}[label=(\alph*)]
\item Use partial fractions to show that $\sum _ { r = 5 } ^ { n } \frac { 3 } { r ^ { 2 } + r - 2 } = \frac { 37 } { 60 } - \frac { 1 } { n } - \frac { 1 } { n + 1 } - \frac { 1 } { n + 2 }$.
\item Write down the value of $\lim _ { n \rightarrow \infty } \left( \sum _ { r = 5 } ^ { n } \frac { 3 } { r ^ { 2 } + r - 2 } \right)$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 2 2021 Q2 [6]}}