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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What are the two main steps in a proof by induction?
💡 Hint: Think about the first step in proving something is true.
Question 2
Easy
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the purpose of the base case in proof by induction?
- To prove the statement for all integers
- To establish the truth for one initial case
- To derive a general formula
💡 Hint: Remember that every proof needs a starting point to build upon.
Question 2
A celebrity in a party knows everyone but is not known by anyone.
- True
- False
💡 Hint: Think about the social dynamics of knowing someone.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove using induction that for every n > 1, n! > 2^n.
💡 Hint: Consider how quickly factorial values grow compared to powers!
Question 2
Prove that for any integer n, n² + n is even.
💡 Hint: Factor to see the evenness clearly.
Challenge and get performance evaluation