OCR Further Pure Core 2 2017 Specimen — Question 3 4 marks

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2017
SessionSpecimen
Marks4
TopicSequences and series, recurrence and convergence
TypeInfinite series convergence and sum
DifficultyStandard +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.
Spec4.06b Method of differences: telescoping series

3
  1. Find \(\sum _ { r = 1 } ^ { n } \left( \frac { 1 } { r } - \frac { 1 } { r + 2 } \right)\).
  2. What does the sum in part (i) tend to as \(n \rightarrow \infty\) ? Justify your answer.

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]}}