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Year 12 Maths Extension 2 (2027) Proof

Induction – Divisibility

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Questions
Question 1
183378
Prove by mathematical induction that \(n^3 + 2n\) is divisible by \(3\) for all positive integers \(n\).
Base \(n=1\): \(3\). Step: if \(k^3+2k = 3M\), then \((k+1)^3+2(k+1) = (k^3+2k) + 3(k^2+k+1) = 3(M+k^2+k+1)\). Divisible by \(3\).

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