Problem 1
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
Solve the recurrence relation f(n) = 4f(n-1) - 4f(n-2) + n2 for f(0) = 2 and f(1) = 5.
(Solution)
Problem 3
Consider the linear homogeneous recurrence relation an = 2an−1 - 2an−2. (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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