Edexcel FP1 Specimen — Question 9

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
SessionSpecimen
TopicProof by induction

9. Use the method of mathematical induction to prove that, for \(n \in \mathbb { Z } ^ { + }\),
  1. \(\left( \begin{array} { c c } 2 & 1
    - 1 & 0 \end{array} \right) ^ { n } = \left( \begin{array} { c c } n + 1 & n
    - n & 1 - n \end{array} \right)\)
  2. \(\mathrm { f } ( n ) = 4 ^ { n } + 6 n - 1\) is divisible by 3 .