Practice - Proof by Induction
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Practice Questions
Test your understanding with targeted questions
What are the two main steps in a proof by induction?
💡 Hint: Think about the first step in proving something is true.
What is the base case for proving that the arithmetic mean is at least the geometric mean for 2 numbers?
💡 Hint: Consider two positive integers and their means.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the purpose of the base case in proof by induction?
💡 Hint: Remember that every proof needs a starting point to build upon.
A celebrity in a party knows everyone but is not known by anyone.
💡 Hint: Think about the social dynamics of knowing someone.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Prove using induction that for every n > 1, n! > 2^n.
💡 Hint: Consider how quickly factorial values grow compared to powers!
Prove that for any integer n, n² + n is even.
💡 Hint: Factor to see the evenness clearly.
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Reference links
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