OCR MEI FP1 2010 June — Question 6

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJune
TopicProof by induction
6 A sequence is defined by \(u _ { 1 } = 2\) and \(u _ { n + 1 } = \frac { u _ { n } } { 1 + u _ { n } }\).
  1. Calculate \(u _ { 3 }\).
  2. Prove by induction that \(u _ { n } = \frac { 2 } { 2 n - 1 }\). Section B (36 marks)
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