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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define proof by induction in your own words.
💡 Hint: Think about how it serves as a mechanism to establish truth across an infinite set.
Question 2
Easy
What must be shown in the base case of an induction proof?
💡 Hint: Consider the first number in the sequence you're working with.
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?
- Establish the base case
- Prove k + 1
- Assume P(k) is true
💡 Hint: Remember, without a strong foundation, the rest doesn't stand.
Question 2
In strong induction, which series of assumptions can you use?
- P(k)
- P(b) through P(k)
- None
💡 Hint: Think about how many cases are at your disposal!
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that for any integer n ≥ 1, n^3 - n is divisible by 6.
💡 Hint: Focus on how n^3 and n can be restructured in forms conducive to divisibility.
Question 2
Using strong induction, prove that any integer n ≥ 12 can be expressed as a sum of 4s and 5s.
💡 Hint: Consider how the addition of either a 4 or 5 affects the total in constructing k + 1.
Challenge and get performance evaluation