Skip to main content
ExamExplained
NSW · Maths Extension 1
Maths Extension 1 study scene
§-Quick questions
NSWMaths Extension 1Proof (ME-P1)

Quick questions on Mathematical induction for inequalities: the technique and the algebraic care

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 is the four-part structure?
Show answer
The structure is the same template as every induction, adapted to an inequality E(n)≤F(n)E(n) \le F(n) (or strict, or reversed) for all n≥n0n \ge n_0:
What is the use-then-strengthen two-step (the core technique)?
Show answer
The technique that makes inductive steps for inequalities work is a two-step chain: use the hypothesis to bound the k+1k + 1 expression, then strengthen that bound until it reaches the target. Concretely, to prove LHS(k+1)>RHS(k+1)\text{LHS}(k + 1) > \text{RHS}(k + 1):
What is direction errors when multiplying?
Show answer
Multiplying both sides by a quantity preserves the inequality only if the quantity is positive; a negative multiplier flips it.

Have a question we have not covered?

This dot-point answer is short enough that we have not extracted many short questions yet. Read the full dot-point answer or ask Mo, our study assistant, in the chat for follow ups.

Openly AI-built from the official NESA syllabus, past papers and marking guides. Not individually reviewed; always check NESAand your school's materials for current rules.

ExamExplained