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Year 12 Maths Extension 2 (2027) Proof

Induction – Identities & Other

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Question 1
183429
Prove by mathematical induction that \(\left(1+\dfrac{1}{1}\right)\left(1+\dfrac{1}{2}\right)\cdots\left(1+\dfrac{1}{n}\right) = n+1\) for all positive integers \(n\).
Base \(n=1\): \(2\). Step: \((k+1)\left(1+\dfrac{1}{k+1}\right) = k+2\).

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