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4 cards from this section. Quick, good the night before a test.
What does the base case in induction verify?
Think about the beginning of the sequence.
Define the inductive step.
What follows after proving the base case?
What is the purpose of the base case in induction?
Think about why we start with a specific case.
True or False: Strong induction requires proving a base case.
Reflect on what's necessary in any induction proof.
Suppose you're asked to prove the sum of the first n odd numbers is n^2 using induction. Outline your proof.
Consider how the next odd number relates to your inductive assumption.
Prove that for all integers n ≥ 1, 2^n > n^2. Discuss the base case and find the value of n for which this holds true.
How does the exponential function compare to polynomials as n grows?
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