Practice - Uniqueness of Solutions for Recurrence Equations
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is a recurrence equation?
💡 Hint: Think about sequences and how their terms relate.
Define initial conditions in the context of recurrence relations.
💡 Hint: Consider what you need to start calculating a sequence.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What defines a linear homogeneous recurrence equation?
💡 Hint: Focus on the structure of the equation.
True or False: All recurrence equations have one and only one solution.
💡 Hint: Think about what happens without fixed starting points.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
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).
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.