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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what a non-homogeneous recurrence equation is?
💡 Hint: Think of how it differs from a homogeneous one.
Question 2
Easy
What is the associated homogeneous relation?
💡 Hint: Recall how we simplify the equation.
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 is the first step to solve a linear non-homogeneous recurrence equation?
- Find the roots of F(n)
- Form the associated homogeneous relation
- Guess the particular solution
💡 Hint: Think about what we do to simplify the original equation.
Question 2
True or False: The particular solution satisfies only the homogeneous part of the recurrence.
- True
- False
💡 Hint: Recall the components of a particular solution.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the recurrence relation a_n = 4a_(n-1) + 2n, derive the general solution.
💡 Hint: Remember the steps of chopping off and combining solutions.
Question 2
If the recurrence is defined as a_n = 5a_(n-1) + 7, determine the structure of your particular solution based on the roots identified.
💡 Hint: Think about what it means when the constant is not a root of the characteristic equation.
Challenge and get performance evaluation