| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Topic | Sequences and series, recurrence and convergence |
| Type | Infinite series convergence and sum |
| Difficulty | Challenging +1.2 This is a Further Maths question requiring partial fractions decomposition and telescoping series techniques. While it involves multiple steps (decompose, find telescoping pattern, simplify to required form, take limit), these are standard Further Pure techniques with no novel insight required. The algebraic manipulation is moderately involved but routine for FM students. |
| Spec | 4.06b Method of differences: telescoping series |
4
\begin{enumerate}[label=(\alph*)]
\item Determine an expression for $\sum _ { r = 1 } ^ { n } \frac { 1 } { r ( r + 1 ) ( r + 2 ) }$ giving your answer in the form $\frac { 1 } { 4 } - \frac { 1 } { 2 } \mathrm { f } ( n )$.
\item Find the value of $\sum _ { r = 1 } ^ { \infty } \frac { 1 } { r ( r + 1 ) ( r + 2 ) }$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q4 [7]}}