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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the base case for proving the statement that the sum of the first n integers is n(n + 1)/2?
💡 Hint: Evaluate the formula when n equals the smallest integer.
Question 2
Easy
Explain what regular induction is.
💡 Hint: Consider the two main steps involved in the process.
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?
- Proving the inductive step
- Establishing the base case
- Concluding the proof
💡 Hint: Think about which step needs to be validated first.
Question 2
True or False: Strong induction only proves the existence of results for previous integers.
- True
- False
💡 Hint: Consider the scope of what strong induction allows.
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 ≥ 1, 2^n > n^2.
💡 Hint: Consider properties of exponential growth versus polynomial growth.
Question 2
Demonstrate that every amount of postal charges greater than 11 can be paid using 3-rupee and 5-rupee coins.
💡 Hint: Think about every integer in this case and how combinations transition logically.
Challenge and get performance evaluation