Practice Constructing Sequence S' (21.1.10) - Catalan Numbers - Derivation of Closed Form Formula
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Constructing Sequence S'

Practice - Constructing Sequence S'

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a bad sequence in the context of sequence S.

💡 Hint: Think of sequences that do not meet the criteria of non-negative sums.

Question 2 Easy

What is the cardinality of set A?

💡 Hint: Remember this set includes all combinations of the 1s and -1s.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What describes a bad sequence?

Has no negative sums
Has at least one occurrence of a negative sum
Is a sequence of only 1s

💡 Hint: Think about what makes a sequence invalid.

Question 2

True or False: The reflection method creates an injective mapping.

True
False

💡 Hint: Reflect on the one-to-one relationship established by this process.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Design a sequence of length 6 involving three 1s and three -1s. Show it's a bad sequence and apply the reflection method to construct S'. What results do you observe in the reconstruction?

💡 Hint: Make sure to track where your sums dip low.

Challenge 2 Hard

Apply subtractive counting to establish a scenario problem with n=5. Create conditions to define valid versus invalid sequences, and derive overall conclusions from counts.

💡 Hint: Think of it like evaluating checks and balances within defined counting principles.

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Reference links

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