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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.