Practice - Proof of Theorem - Part 1
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Practice Questions
Test your understanding with targeted questions
Write the general form of a linear homogeneous recurrence relation of degree 2.
💡 Hint: Think about how each term relates to the previous ones.
What is meant by characteristic roots?
💡 Hint: Reflect on where they come from.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What form does a linear homogeneous recurrence equation typically take?
💡 Hint: Look for how previous terms in the sequence appear.
True or False: The characteristic roots of a recurrence equation can be the same.
💡 Hint: Consider the nature of quadratic equations.
1 more question available
Challenge Problems
Push your limits with advanced challenges
For T(n) = 4T(n-1) - 4T(n-2), derive the characteristic equation and roots. Then find a general solution.
💡 Hint: Follow the steps to construct your polynomial from the recurrence relation.
Given the initial conditions T(0)=2, T(1)=3, find specific constants A and B for T(n) = A * 3^n + B * 1^n.
💡 Hint: Set up simultaneous equations based on initial terms.
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