Edexcel FP1 2012 January — Question 7

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJanuary
TopicProof by induction
7. A sequence can be described by the recurrence formula $$u _ { n + 1 } = 2 u _ { n } + 1 , \quad n \geqslant 1 , \quad u _ { 1 } = 1$$
  1. Find \(u _ { 2 }\) and \(u _ { 3 }\).
  2. Prove by induction that \(u _ { n } = 2 ^ { n } - 1\)
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