Discrete Mathematics
Problem 1: Nonhomogeneous Linear Recurrence Relations (15+15=30 points)
Consider the nonhomogeneous linear recurrence relation an = 3an−1 + 2n .
(a) Show that whether an = −2n+1 is a solution of the given recurrence relation or not. Show your work step by step.
(Solution)
(b) Find the solution with a0 = 1.
(Solution)
Problem 2: Linear Recurrence Relations (35 points)
Find all solutions of the recurrence relation an = 7an−1 - 16an−2 + 12an−3 + n4n with a0 = -2, a1 = 0, and a2 = 5.
(Solution)
Problem 3: Linear Homogeneous Recurrence Relations
Consider the linear homogeneous recurrence relation an = 2an−1 - 2an−2.
(a) Find the characteristic roots of the recurrence relation.
(20+15 = 35 points)
(Solution)
(b) Find the solution of the recurrence relation with a0 = 1 and a1 = 2. (Solution)
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