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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the base case in an induction proof?
💡 Hint: Think about the starting point for proving a statement.
Question 2
Easy
What is the inductive step?
💡 Hint: How do we move from one integer to the next?
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 proof by induction?
- Prove the inductive step
- Establish the base case
- Conclude the proof
💡 Hint: Think about which step must occur before making assumptions.
Question 2
True or False? Strong induction assumes that the property is true for the last case only.
- True
- False
💡 Hint: Recall the assumption differences.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using regular induction, prove that for every positive integer n, 1 + 2 + ... + n = n(n + 1)/2.
💡 Hint: Set up the algebra for LHS and simplify.
Question 2
Use strong induction to prove that any integer n >= 12 can be expressed as a sum of 4s and 5s.
💡 Hint: Think about how to break down k + 1 into the earlier cases.
Challenge and get performance evaluation