Practice - Comparison of Regular and Strong Induction
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Practice Questions
Test your understanding with targeted questions
What is the base case in an induction proof?
💡 Hint: Think about the starting point for proving a statement.
What is the inductive step?
💡 Hint: How do we move from one integer to the next?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the first step in proof by induction?
💡 Hint: Think about which step must occur before making assumptions.
True or False? Strong induction assumes that the property is true for the last case only.
💡 Hint: Recall the assumption differences.
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Challenge Problems
Push your limits with advanced challenges
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.
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.
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