Practice Proof of Theorem - Part 2 - 14.8 | 14. Solving Linear Homogenous Recurrence Equations – Part I | Discrete Mathematics - Vol 2
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14.8 - Proof of Theorem - Part 2

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the general form of a linear homogeneous recurrence relation?

💡 Hint: Look for the structure where the n-th term relates to its predecessors.

Question 2

Easy

Define characteristic roots in the context of recurrence relations.

💡 Hint: Think about how these roots connect to the structure of the recurrence.

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 does the characteristic equation help us identify?

  • The first term of the sequence
  • The characteristic roots
  • The final term of the sequence

💡 Hint: Recall its purpose in the solution process.

Question 2

True or False: All roots in a characteristic equation must be distinct.

  • True
  • False

💡 Hint: Consider instances where roots overlap.

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Challenge Problems

Push your limits with challenges.

Question 1

Consider the recurrence relation S(n) = 2 * S(n-1) + 3 * S(n-2) with S(0) = 1 and S(1) = 4. Find the characteristic roots and derive the general form of the solution.

💡 Hint: Start with the characteristic equation before substituting in initial conditions.

Question 2

Given a recursion with repeated roots, S(n) = S(n-1) + S(n-2) with initial conditions S(0) = 1 and S(1) = 1, show how you would find the nth term.

💡 Hint: Make sure to label your roots correctly when handling repeated instances.

Challenge and get performance evaluation