Year 12 Maths Extension 2 (2027)
Proof
Induction – Series
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Questions
Question 1
183366
Prove by mathematical induction that, for all positive integers \(n\), \[1 + 2 + 3 + \dots + n = \dfrac{n(n+1)}{2}.\]
Base \(n=1\) holds. Assuming for \(k\), adding \(k+1\) gives \(\dfrac{k(k+1)}{2} + (k+1) = \dfrac{(k+1)(k+2)}{2}\). By induction true for all \(n\).
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