OCR C2 2005 January — Question 2

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2005
SessionJanuary
TopicArithmetic Sequences and Series

2 A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by $$u _ { 1 } = 2 \quad \text { and } \quad u _ { n + 1 } = \frac { 1 } { 1 - u _ { n } } \text { for } n \geqslant 1 .$$
  1. Write down the values of \(u _ { 2 } , u _ { 3 } , u _ { 4 }\) and \(u _ { 5 }\).
  2. Deduce the value of \(u _ { 200 }\), showing your reasoning.