Topic 1: Mathematical Induction

1 dot point, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How can we prove that a statement is true for every positive integer without checking infinitely many cases?

Mathematical induction proves a statement for all integers from a base value by establishing a base case and showing each case forces the next.

How to write a rigorous proof by mathematical induction: the base case, the inductive hypothesis, the inductive step, and the formal conclusion, with worked sum and divisibility examples.

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