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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 proof by induction?
💡 Hint: Think about the smallest natural number applicable.
Question 2
Easy
What does the inductive hypothesis assume?
💡 Hint: Consider what you need to prove 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?
- Establishing the base case
- Formulating the hypothesis
- Proving for k + 1
💡 Hint: Think about where you start before building upon your argument.
Question 2
True or False: The inductive hypothesis is the part of the proof where we assume the statement is true for k.
- True
- False
💡 Hint: Consider what is required to build upon your assumption.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the formula for the sum of the first n odd numbers is n^2 using induction.
💡 Hint: Focus on the algebraic manipulation of odd numbers.
Question 2
Show that for any integer n >= 1, 2^n - 1 is divisible by n.
💡 Hint: Factorize and explore the properties of exponential numbers.
Challenge and get performance evaluation