Limits of Sequences definitions Flashcards
Limits of Sequences definitions
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Sequence A list of numbers generated by a rule, with each term corresponding to a discrete input, often following a recognizable pattern. Discrete Input A set of specific, separate values such as 1, 2, 3, used as the domain for sequences instead of a continuous range. Limit The value a sequence approaches as its input grows without bound, revealing long-term behavior. Infinity A concept representing an unbounded quantity, often used to describe the behavior of sequences as inputs increase endlessly. Convergence A property where sequence terms get arbitrarily close to a specific value as the input becomes very large. Divergence A situation where sequence terms fail to approach a single value as the input increases, either oscillating or growing without bound. Oscillation A pattern where sequence values alternate between two or more numbers, preventing approach to a single limit. Table of Values A method of listing sequence terms for various inputs to observe trends and infer long-term behavior. Fraction An expression representing division, often used in sequence formulas to analyze how terms behave as the input increases. Pattern A regular, predictable arrangement in the terms of a sequence, often used to deduce future values. Rational Function A function or sequence term expressed as the ratio of two polynomials, whose behavior at infinity is key to limit analysis. Output The value produced by a sequence for a given input, forming the list of terms. Term An individual element in a sequence, determined by applying the sequence's rule to a specific input. Input The position number in a sequence, typically represented by n, which determines the corresponding term. Behavior at Infinity The trend or pattern shown by sequence terms as the input grows larger and larger.
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