Problem 1: Nonhomogeneous Linear Recurrence Relations
Consider the nonhomogeneous linear recurrence relation an = 3an1 + 2n .
- Show that whether an = 2n+1 is a solution of the given recurrence relation or not. Show your work step by step.
(Solution)
- Find the solution with a0 = 1.
(Solution)
Problem 2: Linear Recurrence Relations
Find all solutions of the recurrence relation an = 7an1 16an2 + 12an3 + n4n with a0 = -2, a1 = 0, and a2 = 5.
(Solution)
| Problem 3: Linear Homogeneous Recurrence RelationsConsider the linear homogeneous recurrence relation an = 2an1 2an2.(a) Find the characteristic roots of the recurrence relation. |
(Solution)
(b) Find the solution of the recurrence relation with a0 = 1 and a1 = 2. (Solution)
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