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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the purpose of the base case in proof by induction?
💡 Hint: Think about where the induction starts.
Question 2
Easy
What is the inductive step in induction?
💡 Hint: What transition do we make from k to k+1?
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 first step in a proof by induction?
- Prove the base case
- Prove the inductive step
- Assume P(k) is true
💡 Hint: What step do we always begin with in the induction framework?
Question 2
True or False: Strong induction requires proving the property for all preceding integers.
- True
- False
💡 Hint: What makes it 'strong' compared to regular induction?
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove by induction that for all integers n, 3^n > n^3 for n >= 3.
💡 Hint: Use properties of exponential functions and inequalities.
Question 2
Show using strong induction that every integer greater than 1 can be expressed as a product of prime numbers.
💡 Hint: Consider prime factorization and how primes build numbers.
Challenge and get performance evaluation