Proving divisibility by induction (HSC SSCE Mathematics Extension 1): Quizzes
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Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
What is mathematical induction used for?
What is mathematical induction used for?
Proving statements for natural numbers
What defines divisibility between integers?
What defines divisibility between integers?
N = d × q for some integer q
What is the closure property in integers?
What is the closure property in integers?
Results of operations are integers
Why is the base case important in induction?
Why is the base case important in induction?
It starts the proof process
What is the inductive step in induction?
What is the inductive step in induction?
Assume true for n=k, prove for n=k+1
What does a complete induction proof require?
What does a complete induction proof require?
Base case and inductive step
What is a common error in induction?
What is a common error in induction?
Incorrect base case initialization
What does proving divisibility by induction show?
What does proving divisibility by induction show?
It holds for all integers n
What is the result of 4^1 - 1?
What is the result of 4^1 - 1?
3, divisible by 3
What is the result of 4^k - 1?
What is the result of 4^k - 1?
3M for some integer M