Practice Proof Of Theorem - Part 1 (14.7) - Solving Linear Homogenous Recurrence Equations – Part I
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Proof of Theorem - Part 1

Practice - Proof of Theorem - Part 1

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Write the general form of a linear homogeneous recurrence relation of degree 2.

💡 Hint: Think about how each term relates to the previous ones.

Question 2 Easy

What is meant by characteristic roots?

💡 Hint: Reflect on where they come from.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What form does a linear homogeneous recurrence equation typically take?

T(n) = a + b
T(n) = a*T(n-1) + b*T(n-2)
T(n) = a*T(n-2) + b*T(n-3)

💡 Hint: Look for how previous terms in the sequence appear.

Question 2

True or False: The characteristic roots of a recurrence equation can be the same.

True
False

💡 Hint: Consider the nature of quadratic equations.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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