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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a recurrence equation?
💡 Hint: Think about sequences and how their terms relate.
Question 2
Easy
Define initial conditions in the context of recurrence relations.
💡 Hint: Consider what you need to start calculating a sequence.
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 defines a linear homogeneous recurrence equation?
- It has multiple solutions.
- It does not include constant terms.
- It is always quadratic.
💡 Hint: Focus on the structure of the equation.
Question 2
True or False: All recurrence equations have one and only one solution.
- True
- False
💡 Hint: Think about what happens without fixed starting points.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the recurrence relation T(n) = 4T(n-1) - T(n-2) with initial conditions T(0) = 1, T(1) = 2, derive T(5).
💡 Hint: Work step by step, substituting previous results until you find T(5).
Question 2
Prove that for the recurrence T(n) = 3T(n-1) with T(0) = 1, the sequence converges to a unique solution by induction.
💡 Hint: Use the assumption to show how it holds for the subsequent term as well.
Challenge and get performance evaluation