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NSWMaths Extension 2Proof (MEX-P2)

Quick questions on Further proof by induction in HSC Mathematics Extension 2: series, divisibility, inequalities, strong induction with multiple base cases, and where ordinary induction fails

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are too few base cases?
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A two-term recurrence needs two base cases; verifying only n=1n = 1 leaves the chain broken at the second term.
What is wrong base case?
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If the statement only holds from n=5n = 5, verifying n=1n = 1 is pointless. Start at the correct n0n_0.
What is sloppy algebra in the step?
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Factorising the k+1k+1 expression to match the target form is where marks are won or lost. Show the manipulation in full.

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