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Series definitions

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  • Sequence
    An ordered list of numbers generated by a specific formula, where each entry corresponds to a particular value of an index.
  • Term
    A single value in an ordered list, found by substituting a specific index into a defining formula.
  • Index
    A variable, often represented by n, that identifies the position of an entry within an ordered list.
  • Factorial
    A product of all positive integers up to a given number, with zero yielding a value of one by definition.
  • Zero Factorial
    A special case in products of consecutive integers, always defined as one, regardless of context.
  • Formula
    A mathematical expression that determines the value of each entry in an ordered list based on its position.
  • Substitution
    The process of replacing a variable in an expression with a specific value to compute a result.
  • Product
    A result obtained by multiplying two or more numbers or expressions together.
  • Square
    A value obtained by multiplying a number by itself, often used in defining patterns in ordered lists.
  • Natural Number
    A positive integer, typically used as the position indicator in ordered mathematical lists.
  • Pattern
    A recognizable regularity in a list of numbers, often revealed by a defining mathematical rule.
  • Calculation
    A step-by-step process of simplifying expressions to determine specific values in a mathematical context.
  • Expression
    A combination of numbers, variables, and operations that represents a specific mathematical idea.
  • Order
    The arrangement of entries in a list according to increasing values of the position indicator.
  • List
    A collection of numbers arranged in a specific sequence, each associated with a unique position.