Applications of mathematical induction (HSC SSCE Mathematics Extension 2): Flashcards
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What is mathematical induction used for?
What is mathematical induction used for?
To prove statements about positive numbers.
Why is mathematical induction important?
Why is mathematical induction important?
It systematically proves statements from specific to general.
What is the base case in induction?
What is the base case in induction?
The initial case that must be proven true.
What is the inductive hypothesis?
What is the inductive hypothesis?
Assuming the statement is true for n = k.
What does the inductive step show?
What does the inductive step show?
It proves the statement for n = k + 1.
What is a common pitfall in induction?
What is a common pitfall in induction?
Mismanaging the base case can lead to errors.
How to prove the sum of first n integers?
How to prove the sum of first n integers?
Use induction to show 1 + 2 + ... + n = n(n+1)/2.
What is a combinatorial proof example?
What is a combinatorial proof example?
Proving handshakes at a meeting with n people.
What should you check in the base case?
What should you check in the base case?
Ensure it is correctly verified and true.
What is a key tip for successful induction?
What is a key tip for successful induction?
Clearly state and prove the inductive step.