Practice Claims About Bad Sequence (21.1.9) - Catalan Numbers - Derivation of Closed Form Formula
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Claims About Bad Sequence

Practice - Claims About Bad Sequence

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the total number of valid sequences of 1's and -1's?

💡 Hint: Think about how many places you can choose for the 1's.

Question 2 Easy

Define a bad sequence in your own words.

💡 Hint: Consider sequences with parentheses or ladder-like paths.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for Catalan numbers?

C(2n
n)/(n+1)
C(2n
n+1)
C(n
2n)

💡 Hint: Recall the conclusion at the end of our session.

Question 2

True or False: Set A is defined to include all legitimate sequences with no restrictions.

True
False

💡 Hint: Think about the restrictions we talked about.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given n = 4, find all valid sequences of 1's and -1's, and verify using the Catalan number formula.

💡 Hint: Write out the sequences; account for each by ensuring partial sums are valid.

Challenge 2 Hard

If the first two positive indices yield a negative sum, demonstrate the reflection method with an example.

💡 Hint: Ask yourself how you can visualize the switch in numbers.

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