| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2017 |
| Session | Specimen |
| Marks | 4 |
| Topic | Sequences and series, recurrence and convergence |
| Type | Infinite series convergence and sum |
| Difficulty | Standard +0.3 This is a straightforward telescoping series question requiring students to write out terms to identify cancellation, then find the limit. While it's Further Maths content, the technique is standard and the algebraic manipulation is minimal, making it slightly easier than an average A-level question overall. |
| Spec | 4.06b Method of differences: telescoping series |
3\\
(i) Find $\sum _ { r = 1 } ^ { n } \left( \frac { 1 } { r } - \frac { 1 } { r + 2 } \right)$.\\
(ii) What does the sum in part (i) tend to as $n \rightarrow \infty$ ? Justify your answer.
\hfill \mbox{\textit{OCR Further Pure Core 2 2017 Q3 [4]}}