Practice - Argument Form of Induction Proof
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Practice Questions
Test your understanding with targeted questions
What does the base case in induction verify?
💡 Hint: Think about the beginning of the sequence.
Define the inductive step.
💡 Hint: What follows after proving the base case?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the purpose of the base case in induction?
💡 Hint: Think about why we start with a specific case.
True or False: Strong induction requires proving a base case.
💡 Hint: Reflect on what's necessary in any induction proof.
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Challenge Problems
Push your limits with advanced challenges
Suppose you're asked to prove the sum of the first n odd numbers is n^2 using induction. Outline your proof.
💡 Hint: 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.
💡 Hint: How does the exponential function compare to polynomials as n grows?
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Reference links
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