ME-P1
Proof by Mathematical Induction
Understand the principle of mathematical induction; prove results for sums, divisibility and inequalities.
Sample questions
- 1.Prove by mathematical induction that 1 + 3 + 5 + … + (2n − 1) = n² for all positive integers n.
- 2.Prove that 3ⁿ − 1 is divisible by 2 for all positive integers n.
Exam weighting
3–4 marks — a proof question appears in almost every Extension 1 paper.
Common student mistakes
- ·Not assuming P(k) is true before proving P(k+1)
- ·Missing the explicit base-case check
- ·Incomplete inductive step — not clearly deriving the k+1 form from the k assumption
Other Extension 1 topics
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