Proof by Induction | Leaving Cert Higher Level Maths | 2025 Paper 1 Q10 (e)

Struggling with Proof by Induction? In this video, we walk through the step-by-step solution for Question 10 (e) from the 2025 Leaving Cert Higher Level Maths Paper 1. Proof by induction can be one of the more repetitive topics in the syllabus, but it’s a vital one to master for the exam. We’ll show you exactly how to structure your answer—from testing for n equals 1 to making your assumption and completing the final proof—so you can pick up full marks on the day. Whether you're studying for your Mocks or the final exam, this guide will help make Proof by Induction that bit easier! Timestamps: 0:00 Introduction to the Question 0:24 Part (i): Finding the value for Pattern 1 0:54 Understanding the recurrence formula 1:33 Part (ii): Proof by Induction – Step 1: Prove for n=1 2:00 Step 2: Make the assumption for n=k 2:20 Step 3: Prove for n=k+1 3:22 Using the given fact in the proof 4:11 Simplifying the equation and concluding 5:39 Final Conclusion and Summary Tags: leaving cert maths, leaving cert higher level maths, proof by induction, 2025 leaving cert maths paper 1, leaving cert maths solutions, maths grinds, irish secondary school maths, project maths ireland, lchl maths paper 1, how to do proof by induction, leaving cert maths question 10