Intro to Proof by Induction (Edexcel A-Level Further Mathematics): Quizzes

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Intro to Proof by Induction
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What does mathematical induction prove?

Statements depending on positive integer nn

What is verified in the base case step?

Statement true for smallest specified nn

What is the inductive hypothesis?

Assume statement true for n=kn=k

What must be done in the inductive step?

Prove true for n=k+1n=k+1 using hypothesis

For proving 2n>1+n2^n > 1+n for all n2n \geq 2, what is the base case?

n=2n=2

In the inductive step, what should you look at first?

How to get LHS of target from assumption

What technique gives another true statement from the assumption?

Multiplying both sides by same value

Why must you state ranges like 'k>0k>0 for k1k \geq 1'?

To justify inequalities hold

What is concluded if true for n=kn=k implies true for n=k+1n=k+1 and base case holds?

True for all integers nn \geq base

How many steps are in a proof by induction?

4

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