Last Updated Sep 27, 2025

Proof by Induction Simplified Revision Notes for Leaving Cert Mathematics

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Learn about Induction for your Leaving Cert Mathematics Exam. This Revision Note includes a summary of Induction for easy recall in your Mathematics exam

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Proof by Induction

Proof by induction is a mathematical technique used to prove that a statement or formula is true for all natural numbers ($n∈\mathbb{N}$) or a specified subset of integers. It is particularly useful for proving propositions involving sequences, inequalities, or formulas.

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Steps for Induction

1. Verify that the statement is true for the initial value of $n$.
2. Assume that $P(k)$ is true for some $k \ge n_0$. This is known as the inductive hypothesis.
3. Using the inductive hypothesis, prove true $P(k+1)$ is true.

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