CMPSC 40 Chapter Notes - Chapter 2.4-2.5: Arithmetic Progression, Continuum Hypothesis, Aleph Number
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2. 4 sequences and summations: individual term relation together with the initial conditions, conflicts with the notation of a set, closed formula = the explicit formula for the terms of the sequence that solves the recurrence. A solution of a recurrence relation is a sequence whose terms satisfy the recurrence relation. A recurrence relation is said to recursively define a sequence. Initial conditions = the specified terms that precede the first term where the recurrence: sequence = a function from a subset of the set of integers (usually either the set or the set to a set. Use notation to denote the image of the integer. Geometric progression = a sequence of the form , where the initial term and the common ratio are real numbers. It is a discrete analogue of the exponential function: arithmetic progression = a sequence of the form. Theorem 1: if and are real numbers and , then:
