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2 cards from this section. Quick, good the night before a test.
What is a recurrence equation?
Think about sequences and how their terms relate.
Define initial conditions in the context of recurrence relations.
Consider what you need to start calculating a sequence.
What defines a linear homogeneous recurrence equation?
Focus on the structure of the equation.
True or False: All recurrence equations have one and only one solution.
Think about what happens without fixed starting points.
Given the recurrence relation T(n) = 4T(n-1) - T(n-2) with initial conditions T(0) = 1, T(1) = 2, derive T(5).
Work step by step, substituting previous results until you find T(5).
Prove that for the recurrence T(n) = 3T(n-1) with T(0) = 1, the sequence converges to a unique solution by induction.
Use the assumption to show how it holds for the subsequent term as well.
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