Practice - Proof Strategy
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Practice Questions
Test your understanding with targeted questions
What is the value of C(2, 1)?
💡 Hint: Think of the number of ways to choose 1 from 2.
Define what a bad sequence is in the context of Catalan numbers.
💡 Hint: Consider what violates the sequence of valid parenthesis.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What do Catalan numbers count?
💡 Hint: Think about the nature of matching pairs.
The reflection method maps bad sequences to valid sequences.
💡 Hint: Consider how reflection alters the sequences.
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Challenge Problems
Push your limits with advanced challenges
Devise an alternate proof for the formula for Catalan numbers without using the reflection method.
💡 Hint: Focus on how smaller sequences of parentheses can combine to form larger ones.
Calculate C(2n, n) for n = 4 and explain how it relates to Catalan numbers.
💡 Hint: Don't forget to apply the formula for C(2n, n) directly!
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Reference links
Supplementary resources to enhance your learning experience.